Testing Nivolumab as a Potential Targeted Treatment in Cancers With Mismatch Repair Deficiency (MATCH-Subprotocol Z1D)

Inclusion Criteria: * Patients must have met applicable eligibility criteria in the Master MATCH Protocol prior to registration to treatment subprotocol * Patients must have mismatch repair deficiency as determined via the MATCH Master Protocol * Women of childbearing potential (WOCBP) receiving nivolumab must agree to use adequate contraception (hormonal or double barrier method of birth control; abstinence) from one week prior to study treatment starting, during treatment, and for a period of 5 months after the last dose of nivolumab. Men receiving nivolumab and who are sexually active with WOCBP must agree to use adequate contraception (hormonal or double barrier method of birth control; abstinence) from one week prior to study treatment starting, during treatment, and for a period of 7 months after the last dose of nivolumab * Patients with hepatitis B virus (HBV) or hepatitis C virus (HCV) infection may be eligible provided they have the following: * There must be no evidence of clinically significant hepatic injury from hepatitis virus infection * For HBV, patients must be on suppressive therapy and have undetectable HBV viral load * For HCV, patients must either be on suppressive therapy for HCV or have already completed therapy thought to have eradicated HCV Exclusion Criteria: * Patients must not have known hypersensitivity to nivolumab or compounds of similar chemical or biologic composition * No prior therapy with anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CD137, anti-OX-40, anti-CD40 or anti-CTLA-4 antibodies (or any other antibody targeting T cell co-regulatory pathways) * Patients with cancers for which nivolumab is approved or becomes approved are excluded (e.g: colorectal cancer, locally advanced or metastatic urothelial carcinoma, unresectable or metastatic melanoma, metastatic non-small cell lung cancer, advanced renal cell carcinoma, classical Hodgkin lymphoma, and recurrent or metastatic squamous cancer of the head and neck) * Must not have received any of the following therapies within four weeks prior to the first dose of the study drug: IL-2, interferon, or other non-study immunotherapy regimens or immunosuppressive agents * Must not have a history of toxic epidermal necrolysis (Stevens-Johnson syndrome) * Must not have received growth factors, including but not limited to granulocyte-colony stimulating factor (G-CSF), granulocyte macrophage-colony stimulating factor (GM-CSF), erythropoietin, etc. within 2 weeks of study drug administration. Use of such agents while on study is also prohibited. Prior use of growth factors should be documented in the patient's medical history * Must not have a history of any autoimmune disease: inflammatory bowel disease, (including ulcerative colitis and Crohn's disease), rheumatoid arthritis, systemic progressive sclerosis (scleroderma), systemic lupus erythematosus (SLE) autoimmune vasculitis (e.g., Wegener's Granulomatosis), central nervous system (CNS) or motor neuropathy considered to be of autoimmune origin (e.g., Guillain-Barre syndrome, myasthenia gravis, multiple sclerosis). Patients are permitted to enroll if they have vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger (precipitating event). Entry of patients with autoimmune diagnoses not listed here must be approved by the protocol chair * Must not be on supplemental home oxygen * Must not have evidence of interstitial lung disease * Patients with a requirement for steroid treatment or other immunosuppressive treatment: Patients will be excluded if they have a condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) within 14 days of study drug administration. Inhaled or topical steroids and adrenal replacement doses \> 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease * No history of severe hypersensitivity reaction to any monoclonal antibody