Atezolizumab With or Without Eribulin Mesylate in Treating Patients With Recurrent Locally Advanced or Metastatic Urothelial Cancer

Inclusion Criteria: * Males or females age \> or = 18 years at the time of informed consent. Because no dosing or adverse event data are currently available on the use of atezolizumab in combination with eribulin in patients \< 18 years of age, children are excluded from this study * Histologically- or cytologically-confirmed diagnosis of locally advanced/unresectable (inoperable or not amenable to surgical treatment) and/or metastatic transitional cell urothelial cancer of the renal pelvis, ureter, urinary bladder, or urethra * Presence of measurable disease meeting the following criteria: * At least one lesion of \>= 1.0 cm in long axis diameter for non-lymph nodes or \>= 1.5 cm in short axis diameter for lymph nodes that is serially measurable according to RECIST 1.1 using either computerized tomography or magnetic resonance imaging or panoramic and close-up color photography with caliper measurement; if there is only one target lesion and it is a not a lymph node, it should have a long-axis diameter of at least 1.5 cm * Lesions that have had radiotherapy must show radiographic evidence of disease progression based on RECIST 1.1 may be deemed a target lesion * Archival paraffin-embedded invasive tumor tissue or newly obtained biopsy must be available prior to the first dose of study drug for biomarker analysis; patients must be offered sequential biopsies at baseline and 6 weeks unless in the opinion of the trial principal investigator (PI) this would be hazardous; recent data suggest discordance between primary tumor and tumor from recurrence or metastasis with high percentages of PD-L1 SP142 positive immune cells after recurrence * PD-L1 status determined centrally by HistogeneX, which is funded by the study, must be available before randomization of the patient to allow for stratification; COMMERCIAL ASSESSMENT OF PD-L1 STATUS OBTAINED LOCALLY AT THE SITE WILL NOT SATISFY ELIGIBILITY CRITERIA * New, progressive or recurrent disease occurring * During or within 12 months of treatment with a platinum containing regimen (cisplatin or carboplatin or novel platinum) in either in the metastatic or perioperative setting * In first-line patients defined as cisplatin-ineligible based on renal impairment (creatinine clearance calculated by Cockcroft-Gault method \< 60 ml/min), at least grade 2 hearing loss and/or Eastern Cooperative Oncology Group (ECOG) status of 2; these patients will be chemotherapy naive or have received platinum based therapy in the adjuvant or neoadjuvant setting more than 12 months prior to study entry * May have received up to two prior lines of chemotherapy for advanced disease * Adequate recovery from any adverse events resulting from prior anti-neoplastic treatment including chemotherapy, biological therapy, targeted small molecule therapy, radiation therapy, and surgery as determined by the investigator (and in consultation with the study PI); in most instances, adequate recovery is resolution to =\< grade 1 except for alopecia of any grade, grade 2 neuropathy and/ or any grade hearing loss * Subjects with known brain metastases will be eligible if they have completed the primary brain therapy (such as whole brain radiotherapy, stereotactic radiosurgery, or complete surgical resection) and if they have remained clinically stable, asymptomatic, and off of steroids for at least 28 days * Life expectancy of \>= 12 weeks * Subjects must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2 (Karnofsky \>= 60%) * Leukocytes \>= 2,500/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 75,000/mcL * Hemoglobin \>= 8 g/dL * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) (however, patients with known Gilbert disease who have serum bilirubin level =\< 3 x ULN may be enrolled) * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x ULN (AST and/or ALT =\< 5 x ULN for patients with liver involvement) * Alkaline phosphatase =\< 2.5 x ULN (=\< 5 x ULN for patients with documented liver involvement or bone metastases) * Creatinine clearance \>= 20 mL/min/1.73 m\^2 by Cockcroft-Gault * International normalized ratio (INR) and activated partial thromboplastin time (aPTT) =\< 1.5 x ULN (this applies only to patients who do not receive therapeutic anticoagulation; patients receiving therapeutic anticoagulation, such as low-molecular-weight heparin or warfarin, should be on a stable dose) * All females must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of beta-human chorionic gonadotropin \[B-hCG\]) at the screening visit and the baseline visit; a pregnancy test needs to be performed within 72 hours of the first dose of study drug * Administration of atezolizumab and eribulin may have an adverse effect on pregnancy and poses a risk to the human fetus, including embryo-lethality; women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 5 months (150 days) after the last dose of study agent; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately * Male subjects who are partners of women of childbearing potential must use a condom and spermicide and their female partners if of childbearing potential must use a highly effective method of contraception beginning at least 1 menstrual cycle prior to starting study drug(s), throughout the entire study period, and for 150 days after the last dose of study drug, unless the male subjects are totally sexually abstinent or have undergone a successful vasectomy with confirmed azoospermia or unless the female partners have been sterilized surgically or are otherwise proven sterile * Ability to understand and the willingness to sign a written informed consent document * Subject must be willing and able to comply with all aspects of the protocol * Patients positive for human immunodeficiency virus (HIV) are allowed on study, but HIV-positive patients must have: * A stable regimen of highly active anti-retroviral therapy (HAART) using combination retroviral agents which are not CYP3A4 inducers or inhibitors * No requirement for concurrent antibiotics or antifungal agents for the prevention of opportunistic infections * A CD4 count above 250 cells/mcL and an undetectable HIV viral load on standard polymerase chain reaction (PCR)-based tests Exclusion Criteria: * Patients with prior allogeneic bone marrow transplantation or prior solid organ transplantation * Patients who have had chemotherapy within 3 weeks or radiotherapy or targeted therapy 2 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events (other than alopecia) due to agents administered more than 4 weeks earlier; however, the following therapies are allowed: * Hormone-replacement therapy or oral contraceptives * Herbal therapy \> 1 week prior to cycle 1, day 1 (herbal therapy intended as anticancer therapy must be discontinued at least 1 week prior to cycle 1, day 1) * Palliative radiotherapy for bone metastases \> 2 weeks prior to cycle 1, day 1 * Prior treatment with anti-PD-1, or anti-PD-L1 therapeutic antibody or pathway-targeting agents or eribulin * Patients who have received prior treatment with anti-CTLA-4 may be enrolled, provided the following requirements are met: * Minimum of 12 weeks from the first dose of anti-CTLA-4 and \> 6 weeks from the last dose * No history of severe immune-related adverse effects from anti-CTLA-4 (National Cancer Institute \[NCI\] Common Terminology Criteria for Adverse Events \[CTCAE\] version 5.0) * Treatment with any other investigational agent within 4 weeks prior to cycle 1, day 1 * Treatment with systemic immunostimulatory agents (including, but not limited to, interferon \[IFN\]-alpha or interleukin \[IL\]-2) within 6 weeks prior to cycle 1, day 1 * Treatment with systemic immunosuppressive medications (including, but not limited to, prednisone, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor \[anti-TNF\] agents) within 2 weeks prior to cycle 1, day 1 * Patients who have received acute, low dose, systemic immunosuppressant medications (e.g., a one-time dose of dexamethasone for nausea) may be enrolled * The use of inhaled corticosteroids and mineralocorticoids (e.g., fludrocortisone) for patients with orthostatic hypotension or adrenocortical insufficiency is allowed * Patients taking bisphosphonate therapy for symptomatic hypercalcemia; use of bisphosphonate therapy for other reasons (e.g., bone metastasis or osteoporosis) is allowed * Patients requiring treatment with a receptor activator of nuclear factor kappa-B ligand (RANKL) inhibitor (e.g. denosumab) who cannot discontinue it before treatment with atezolizumab * Patients with known primary central nervous system (CNS) malignancy or symptomatic CNS metastases are excluded, with the following exceptions: * Patients with asymptomatic untreated CNS disease may be enrolled, provided all of the following criteria are met: * Evaluable or measurable disease outside the CNS * No metastases to brain stem, midbrain, pons, medulla, cerebellum, or within 10 mm of the optic apparatus (optic nerves and chiasm) * No history of intracranial hemorrhage or spinal cord hemorrhage * No ongoing requirement for dexamethasone for CNS disease; patients on a stable dose of anticonvulsants are permitted * No neurosurgical resection or brain biopsy within 28 days prior to cycle 1, day 1 * Patients with asymptomatic treated CNS metastases may be enrolled, provided all the criteria listed above are met as well as the following: * Radiographic demonstration of improvement upon the completion of CNS directed therapy and no evidence of interim progression between the completion of CNS directed therapy and the screening radiographic study * No stereotactic radiation or whole-brain radiation within 28 days prior to cycle 1, day 1 * Screening CNS radiographic study \>= 4 weeks from completion of radiotherapy and \>= 2 weeks from discontinuation of corticosteroids * Known hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies * History of severe allergic, anaphylactic, or other hypersensitivity reactions to chimeric or humanized antibodies or fusion proteins or eribulin * History of allergic reactions attributed to compounds of similar chemical or biologic composition to other agents used in study * Known additional malignancy that is progressing or requires active treatment excepting basal cell carcinoma of the skin, squamous cell carcinoma of the skin that has undergone potentially curative therapy, or in situ cancer; patients with another known malignancy are allowed as long that other cancer is in clinical remission for at least 2 years prior to cycle 1 (C1) day 1 (D1) * History of significant cardiovascular disease, defined as: * Congestive heart failure greater than New York Heart Association (NYHA) class III according to the NYHA functional classification * Unstable angina or myocardial infarction within 6 months of enrollment * Serious cardiac arrhythmia * A prolonged QT/corrected QT (QTc) interval calculated with Frederica's formula (QTcF \> 450 ms) demonstrated on electrocardiography (ECG) at screening or baseline; a history of risk factors for torsade de pointes (e.g., heart failure, hypokalemia, family history of long QT syndrome) or the use of concomitant medications that prolonged the QT/QTc interval * Autoimmune disease that has required systemic treatment in past 2 years * Clinically significant illness that requires medical treatment within 8 weeks or a clinically significant infection that requires medical treatment within 4 weeks of dosing * History of organ allograft * Active hepatitis b virus (positive hepatitis b surface antigen) or active hepatitis c virus (measurable viral ribonucleic acid \[RNA\] load with polymerase chain reaction) infection * Known intolerance to either of the study drugs (or any of the excipients) * Any medical or other condition which, in the opinion of the investigator, would preclude participation in a clinical trial or the investigator's belief that the subject is medically unfit to receive eribulin mesylate and atezolizumab or unsuitable for any other reason * Known clinically significant liver disease, including active viral, alcoholic, or other hepatitis; cirrhosis; fatty liver; and inherited liver disease * Patients with past or resolved hepatitis B infection (defined as having a negative hepatitis B surface antigen \[HBsAg\] test and a positive anti-HBc \[antibody to hepatitis B core antigen\] antibody test) are eligible * Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV RNA * History or risk of autoimmune disease, including, but not limited to, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener's granulomatosis, Sjogren's syndrome, Bell's palsy, Guillain-Barre syndrome, multiple sclerosis, autoimmune thyroid disease, vasculitis, or glomerulonephritis * Patients with a history of autoimmune hypothyroidism on a stable dose of thyroid replacement hormone may be eligible * Patients with controlled type 1 diabetes mellitus on a stable insulin regimen may be eligible * Patients with eczema, psoriasis, lichen simplex chronicus of vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis would be excluded) are permitted provided that they meet the following conditions: * Patients with psoriasis must have a baseline ophthalmologic exam to rule out ocular manifestations * Rash must cover less than 10% of body surface area (BSA) * Disease is well controlled at baseline and only requiring low potency topical steroids (e.g., hydrocortisone 2.5%, hydrocortisone butyrate 0.1%, fluocinolone 0.01%, desonide 0.05%, alclometasone dipropionate 0.05%) * No acute exacerbations of underlying condition within the last 12 months (not requiring psoralen plus ultraviolet A radiation \[PUVA\], methotrexate, retinoids, biologic agents, oral calcineurin inhibitors; high potency or oral steroids) * History of idiopathic pulmonary fibrosis, pneumonitis (including drug induced), organizing pneumonia (i.e., bronchiolitis obliterans, cryptogenic organizing pneumonia, etc.), or evidence of active pneumonitis on screening chest computed tomography (CT) scan; history of radiation pneumonitis in the radiation field (fibrosis) is permitted * Patients with active tuberculosis (TB) are excluded * Severe infections within 4 weeks prior to cycle 1, day 1, including, but not limited to, hospitalization for complications of infection, bacteremia, or severe pneumonia * Signs or symptoms of infection within 2 weeks prior to cycle 1, day 1 * Received oral or intravenous (IV) antibiotics within 2 weeks prior to cycle 1, day 1; patients receiving prophylactic antibiotics (e.g., for prevention of a urinary tract infection or chronic obstructive pulmonary disease) are eligible * Major surgical procedure within 28 days prior to cycle 1, day 1 or anticipation of need for a major surgical procedure during the course of the study * Administration of a live, attenuated vaccine within 4 weeks before cycle 1, day 1 or anticipation that such a live, attenuated vaccine will be required during the study and up to 5 months after the last dose of atezolizumab * Influenza vaccination should be given during influenza season only (approximately October to March); patients must not receive live, attenuated influenza vaccine within 4 weeks prior to cycle 1, day 1 or at any time during the study * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study because atezoluzumab and eribulin have not been formally tested in pregnancy but have potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with atezoluzumab and eribulin, breastfeeding should be discontinued if the mother is treated with atezolizumab and eribulin and for 2 weeks after last dose