Atezolizumab, Cobimetinib, and Eribulin in Treating Patients With Chemotherapy Resistant Metastatic Inflammatory Breast Cancer

Inclusion Criteria: * Signed informed consent form (ICF) and comply with the requirements of the study protocol * Eastern Cooperative Oncology Group (ECOG) performance status 0-1 * Confirmed diagnosis of inflammatory breast cancer according to international consensus criteria: (1) onset: rapid onset of breast erythema, edema, and/or peau d'orange, and/or warm breast, with or without an underlying breast mass (2) duration: history of such findings no more than 6 months (3) extent: erythema occupying at least 1/3 of whole breast (4) pathology: pathologic confirmation of invasive carcinoma * Patients with recurrent or metastatic IBC after standard systemic therapy are eligible; patients who have disease progression while receiving standard anthracycline or taxane based neoadjuvant therapy are also eligible. a. patients with HER2-positive disease must have had at least 2 lines of anti-HER2 therapy, including Perjeta and Kadcyla; b. prior eribulin treatment is allowed * At least one metastatic lesion amendable for biopsy (core, punch, or fine needle aspiration \[FNA\]); if the patient only has lymph nodes, these are considered amenable but will not be biopsied * At least one site of measurable disease (per Response Evaluation Criteria in Solid Tumors \[RECIST\] 1.1), local or distant * Any estrogen receptor (ER), progesterone receptor (PR), HER2 status * Absolute neutrophil count (ANC) \>= 1500 cells/uL (obtained within 14 days prior to the first study treatment \[PD window day 1\]) * White blood cell (WBC) counts \> 2500/uL (obtained within 14 days prior to the first study treatment \[PD window, day 1\]) * Lymphocyte count \>= 300/uL (obtained within 14 days prior to the first study treatment \[PD window day 1\]) * Platelet count \>= 100,000/uL (obtained within 14 days prior to the first study treatment \[PD window day 1\]) * Hemoglobin \>= 9.0 g/dL (obtained within 14 days prior to the first study treatment \[PD window day 1\]) * Total bilirubin =\< 1.5 x upper limit of normal (ULN) with the following the exception: Patients with known Gilbert disease who have serum bilirubin level =\< 3 x ULN may be enrolled (obtained within 14 days prior to the first study treatment \[PD window, day 1\]) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 x ULN with the exception: Patients with liver involvement: AST and/or ALT =\< 5 x ULN (obtained within 14 days prior to the first study treatment \[PD window, day 1\]) * Alkaline phosphatase =\< 2.5 x ULN with the exception: Patients with documented liver involvement or bone metastases: alkaline phosphatase =\< 5 x ULN (obtained within 14 days prior to the first study treatment \[PD window, day 1\]) * Serum creatinine =\< 1.5 x ULN or creatinine clearance \>= 50 mL/min on the basis of the Cockcroft-Gault glomerular filtration rate estimation (obtained within 14 days prior to the first study treatment \[PD window, day 1\]) * For women of childbearing potential or male subjects: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive methods that result in a failure rate of \< 1% per year, during the treatment period and for at least 5 months after the last dose of treatment * International normalized ratio (INR) and activated partial thromboplastin time (aPTT) =\< 1.5 x ULN for 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 * Left ventricular ejection fraction \>= 50% measured by multigated acquisition (MUGA) scan or echocardiogram Exclusion Criteria: * Any approved anticancer therapy for treatment purpose is not allowed, or need to be stopped at least 2 weeks prior to initiation of study treatment; however, the following are allowed: a. endocrine therapy (selective estrogen receptor modulator \[SERM\], aromatase inhibitor, fulvestrant) b. palliative radiotherapy for bone metastases \> 1 week prior to study treatment c. stable brain metastasis and asymptomatic treated central nervous system (CNS) metastases are allowed, patient must show stable disease by CNS radiographic study \>= 4 weeks from completion of radiotherapy and \>= 2 weeks from discontinuation of corticosteroids * Adverse events (AEs) from prior anticancer therapy that have not resolved to grade =\< 1 except for alopecia and neuropathy * Grade 3 or above neuropathy induced from prior treatment, that is not resolved to grade 2 or below despite best supportive care * Known clinically significant liver disease, including active viral, alcoholic, or other hepatitis; cirrhosis; fatty liver; and inherited liver disease * Pregnancy, lactation, or breastfeeding * Known hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies * Inability to comply with study and follow-up procedures * Active or history of autoimmune disease or immune deficiency, including, but not limited to, myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, antiphospholipid antibody syndrome, Wegener granulomatosis, Sjogren's syndrome, Guillain-Barre syndrome, or multiple sclerosis, with the following exception: a. patients with a history of autoimmune hypothyroidism who are on thyroid replacement hormone are eligible for the study; b. patients with controlled type 1 diabetes mellitus who are on an insulin regimen are eligible for the study; c. 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 are met: i. rash must cover \< 10% of body surface area.; ii. disease is well controlled at baseline and requires only low-potency topical corticosteroids; iii. no occurrence of acute exacerbations of the underlying condition requiring psoralen plus ultraviolet A radiation, methotrexate, retinoids, biologic agents, oral calcineurin inhibitors, or high potency or oral corticosteroids within the previous 12 months * Acute exacerbations of underlying condition within the last 12 months (requiring psoralen plus ultraviolet A radiation \[PUVA\], methotrexate, retinoids, biologic agents, oral calcineurin inhibitors; high potency or oral steroids) * Known 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 * Any other diseases, metabolic dysfunction, physical examination finding, or clinical laboratory finding giving reasonable suspicion of a disease or condition that contraindicates the use of an investigational drug or that may affect the interpretation of the results or render the patient at high risk from treatment complications * Known history of human immunodeficiency virus (HIV) infection or active hepatitis B (chronic or acute) or hepatitis C infection; but: a. patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction (PCR) is negative for hepatitis C virus (HCV) RNA; b. 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, but should sample for hepatitis B virus (HBV) DNA and referral to virologist to monitor for HBV reactivation * Active tuberculosis based on history, symptoms, physical exam, imaging * Severe infections within 4 weeks prior to study treatment, including but not limited to hospitalization for complications of infection, bacteremia, or severe pneumonia * Signs or symptoms of infection within 2 weeks prior to study treatment * Received oral or IV antibiotics within 2 weeks prior to study treatment * 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 study treatment or anticipation of need for a major surgical procedure during the course of the study * Patients must agree not to receive any live, attenuated influenza vaccine (e.g., FluMist) within 28 days prior to receiving study treatment, during treatment or within 5 months following the last dose of atezolizumab * Malignancies other than the disease under study within 5 years prior to study treatment, with the exception of those with a negligible risk of metastasis or death and with expected curative outcome (such as adequately treated carcinoma in situ of the cervix, basal or squamous cell skin cancer, or ductal carcinoma in situ treated surgically with curative intent) or undergoing active surveillance per standard-of-care management (e.g., chronic lymphocytic leukemia Rai Stage 0) * COBIMETINIB-SPECIFIC EXCLUSION CRITERIA (ONLY FOR COHORT I): * History of or evidence of retinal pathology on ophthalmologic examination that is considered a risk factor for neurosensory retinal detachment/central serous chorioretinopathy (CSCR), retinal vein occlusion (RVO), or neovascular macular degeneration * Patients will be excluded if they currently have the following risk factors for retinal vein occlusion (RVO): (1) uncontrolled glaucoma with intra-ocular pressures \>= 21 mmHg (2) serum cholesterol \>= grade 2 (3) hypertriglyceridemia \>= grade 2 (4) hyperglycemia (fasting) \>= grade 2 * Patients with congestive heart failure, congenital long QT syndrome; bradyarrhythmias, drugs known to prolong the QT interval unless the principal investigator and/or attending physician deems the risk for QT prolongation to be low * The following foods/supplements are prohibited at least 7 days prior to initiation of and during study treatment: (1) St. John's wort or hyperforin (potent CYP3A4 enzyme inducer) (2) grapefruit juice (potent cytochrome P450 CYP3A4 enzyme inhibitor) * ATEZOLIZUMAB-RELATED EXCLUSION CRITERIA: * Prior treatment with anti-PD-1, or anti-PD-L1 therapeutic antibody or pathway targeting agents: (a) patients who have received prior treatment with anti·CTLA-4 may be enrolled, provided the following requirements are met: (i) minimum of 12 weeks from the first dose of anti-CTLA-4 and \> 6 weeks from the last dose; (ii) no history of severe immune-related adverse effects from anti-CTLA 4 (National Cancer Institute \[NCI\] Common Terminology for Cancer Adverse Effects CTCAE\] grade 3 and 4) * Treatment with systemic immunostimulatory agents (including but not limited to interferon \[IFN\]-a or interleukin \[IL\]-2) within 6 weeks or five half-lives of the drug (whichever is shorter) prior to study treatment * Treatment with investigational agent within 4 weeks prior to study treatment (or within five half lives of the investigational product, whichever is longer) * 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 study treatment; a. patients who have received acute, low dose, systemic immunosuppressant medications (e.g., a one-time dose of dexamethasone for nausea) may be enrolled; b. the use of inhaled corticosteroids and mineralocorticoids (e.g., fludrocortisone) for patients with orthostatic hypotension or adrenocortical insufficiency is allowed * History of severe allergic, anaphylactic, or other hypersensitivity reactions to chimeric or humanized antibodies or fusion proteins * Patients with prior solid organ transplantation on anti-immunosuppressant