Atezolizumab and CYT107 in Treating Participants With Locally Advanced, Inoperable, or Metastatic Urothelial Carcinoma

Inclusion Criteria: * Patients must have histologically or cytologically documented locally advanced/inoperable or metastatic urothelial bladder carcinoma (UBC), including renal pelvis, ureters, urinary bladder, and urethra * Note: Mixed histology tumors allowed if predominant histology is urothelial carcinoma * Note: Small cell or neuroendocrine carcinoma is not allowed if predominant * Patients must have recurrent disease after any prior platinum-based chemotherapy regimen * Patients must have measurable disease per RECIST 1.1 assessed by computed tomography (CT) scan or magnetic resonance imaging (MRI) * ECOG performance status =\< 2 (Karnofsky \>= 60%) * Patients must have a life expectancy of greater or equal to 12 weeks * Leukocytes \>= 2,500/mcL * Absolute neutrophil count \>= 1,000/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 8 g/dL * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) (however, patients with known Gilbert's 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 \>= 30 mL/min/1.73 m\^2 by Cockcroft-Gault * At the discretion of the treating physician, a 24-hour urine creatinine clearance could be obtained and utilized as the gold standard if creatinine clearance by Cockcroft-Gault is \< 30, and prevents patient enrollment on the trial * 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) * Patients must provide tissue from an archival tumor sample (obtained within 2 years from screening visit) or newly obtained core, punch, or excisional biopsy of a tumor lesion if deemed relatively safe and technically feasible * Female patients of childbearing potential must have a negative urine or serum pregnancy test within 72 hours before receiving the first dose of study agent(s); if the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required; * Administration of atezolizumab may have an adverse effect on pregnancy and poses a risk to the human fetus, including embryo-lethality; CYT107 has not been tested for reproductive toxicity yet and may expose to the same risk; women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) before 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 * Patients must have the ability to understand and the willingness to sign a written informed consent document * Patients positive for human immunodeficiency virus (HIV) are allowed on study, but HIV-positive patients must have: * A stable regimen of highly active antiretroviral therapy (HAART) * 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 or radiotherapy within 2 weeks (4 weeks for nitrosoureas or systemic mitomycin C) before the initiation of study treatment * Patients who have received more than 2 systemic cytotoxic chemotherapy regimens for metastatic urothelial carcinoma * Note: Prior perioperative chemotherapy is allowed and is not counted as a line of therapy if patient relapsed \>= 12 months later and received additional platinum-based chemotherapy for metastatic disease * Patients who have not recovered from adverse events (other than alopecia) due to agents administered more than 4 weeks earlier (i.e., have residual toxicities \> grade 1); however, the following therapies are allowed: * Hormone-replacement therapy or oral contraceptives * Herbal therapy \>= 1 week before initiation of study treatment (herbal therapy intended as anticancer therapy must be discontinued at least 1 week before initiation of study treatment) * Palliative radiotherapy for bone metastases \> 2 weeks before initiation of study treatment * Patients who have received prior treatment with anti-PD-1, or anti-PD-L1 therapeutic antibody, or pathway -targeting agents * 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 \[CTCAE\] grade 3 and 4) * Patients who have received treatment with any other investigational agent within 4 weeks before initiation of study treatment * Patients who have received treatment with systemic immunostimulatory agents (including, but not limited to, interferon \[IFN\]-alpha or interleukin \[IL\]-2) within 6 weeks before initiation of study treatment * Patients who have received treatment with systemic immunosuppressive medications (including, but not limited to, oral prednisone ( \> 10 mg/day or equivalent), cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor \[anti TNF\] agents) within 2 weeks before initiation of study treatment * 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 * Note: Use of bisphosphonate therapy for other reasons (e.g., bone metastasis or osteoporosis) is allowed * 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 before initiation of study treatment * 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 before initiation of study treatment * Screening CNS radiographic study \>= 4 weeks from completion of radiotherapy and \>= 2 weeks from discontinuation of corticosteroids * Note: Patients with CNS metastases enrolled on trial must also have a brain MRI imaging at all standard radiologic evaluation timepoints * Patients with known hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies * Patients who have a history of severe allergic, anaphylactic, or other hypersensitivity reactions to chimeric or humanized antibodies or fusion proteins * Patients with known clinically significant liver disease, including active viral, alcoholic, or other hepatitis; cirrhosis; fatty liver/nonalcoholic fatty liver disease (NAFLD)/nonalcoholic steatohepatitis (NASH); 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 is negative for HCV ribonucleic acid (RNA) * Patients with active underlying autoimmune disease requiring systemic immunosuppressive medication (oral prednisone \> 10 mg/day or equivalent). Topical, inhaled, or intra-articular steroids or physiologic endocrine replacement (insulin, levothyroxine, etc.) are permitted. Patients with a history of autoimmune disease that is not currently active require consultation with the protocol principal investigator (PI) and/or Cancer Immunotherapy Trials Network (CITN) Coordinating Center * Patients who have a history of idiopathic pulmonary fibrosis, pneumonitis (including drug induced), organizing pneumonia (bronchiolitis obliterans, cryptogenic organizing pneumonia, etc.), or evidence of active pneumonitis on screening chest CT scan; history of radiation pneumonitis in the radiation field (fibrosis) is permitted * Patients who have known additional malignancies other than UBC within 2 years before initiation of study treatment; exceptions include malignancies with a negligible risk of metastasis or death and treated with expected curative outcome (e.g., non-melanomatous skin cancers), or localized prostate cancer treated with curative intent and absence of prostate-specific antigen (PSA) relapse or incidental prostate cancer * Patients with active tuberculosis (TB) * Patients who have leptomeningeal disease * Patients who have severe infections within 4 weeks before initiation of study treatment, including, but not limited to, hospitalization for complications of infection, bacteremia, or severe pneumonia; * Exception: Uncomplicated urinary tract infection will not be considered as a severe infection in these patients * Patients who have signs or symptoms of infection within 2 weeks before initiation of study treatment * Patients who have received oral or IV antibiotics within 2 weeks before initiation of study treatment; patients receiving prophylactic antibiotics (e.g., for prevention of a urinary tract infection or chronic obstructive pulmonary disease) are eligible * Patients who have major surgical procedure, other than for diagnosis, within 28 days before initiation of study treatment or anticipation of need for a major surgical procedure during the course of the study * Patients who have had a live, attenuated vaccine within 4 weeks before initiation of study treatment 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 before initiation of study treatment or at any time during the study * Uncontrolled intercurrent illness including, but not limited to, symptomatic congestive heart failure (New York Heart Association class III or IV), unstable angina pectoris, cardiac arrhythmia, recent myocardial infarction (within the last 6 months), or psychiatric illness/social situations that would limit compliance with study requirements * Prisoners or subjects who are compulsorily detained (involuntarily incarcerated) for treatment of either a psychiatric or medical (e.g., infectious) illness