Nivolumab for Relapsed, Refractory, or Detectable Disease Post Chimeric Antigen Receptor T-cell Treatment in Patients With Hematologic Malignancies

Inclusion Criteria: * Diagnosis of the following tumor types * Non Hodgkin-lymphoma, including: * Diffuse large B-cell lymphoma: Histopathologic confirmation * Mantle cell lymphoma: Histopathologic confirmation * Follicular lymphoma, all grades: Histopathologic confirmation * Marginal zone lymphoma: Histopathologic confirmation * Chronic lymphocytic leukemia: Histopathologic or flow cytometric confirmation * Multiple myeloma: Histopathologic or flow confirmation * Relapsed, refractory, or detectable disease after treatment with chimeric antigen receptor T-cells \* Multiple Myeloma: patients must have exhausted all treatment options known to provide clinical benefit, and are refractory to a minimum of 3 prior lines of therapy (including an immunomodulatory imide drug \[IMiD\], proteasome inhibitor \[PI\], or anti-CD38 monoclonal antibody) * Have measurable disease, defined by histology: * Non-Hodgkin's lymphoma, based on presence of lesions \>= 1.5 cm that can be accurately measured in 2 dimensions by computed tomography (CT) (preferred) or magnetic resonance imaging (MRI), and are not included in any prior field of radiation therapy * Chronic lymphocytic leukemia: circulating lymphocytes \>= 5,000 / mm\^3 * Multiple myeloma, based on the International Myeloma Working Group (IMWG) criteria of having one or more of the following findings: * Serum M protein \>= 1.0 g/dL * Urine M protein \>= 200 mg/24 hours * Involved serum free light chain level \>= 10 mg/dL with abnormal kappa/lambda ratio * Measurable biopsy-proven plasmacytomas (\>= 1 lesion has a single diameter \>= 2 cm) * Bone marrow plasma cells \>= 30% * Age 18 years and older, and have the capacity to give informed consent * Anticipated survival of \> 3 months * Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 * Post CAR T cell receipt of intervening palliative radiation therapy is allowed * Estimated glomerular filtration rate (eGFR) \>= 20 ml/min * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 3 x upper limit of normal (ULN) * Total bilirubin =\< 2 x ULN * Absolute neutrophil count (ANC) \>= 1,000/uL * Platelets \>= 50,000/uL * Hemoglobin \>= 8 g/dL Exclusion Criteria: * Receipt of intervening therapy after CAR T-cell infusion * History of another primary malignancy that has not been in remission for at least 1 year (with the exception of non-melanoma skin cancer, curatively treated localized prostate cancer, curatively treated superficial bladder cancer and cervical carcinoma in site on biopsy or a squamous intraepithelial lesion on papanicolaou \[PAP\] smear) * Active hepatitis B, hepatitis C at time of screening * Known (human immunodeficiency virus \[HIV\]) seropositivity * Subjects with uncontrolled infection * Concurrent use of other anticancer agents or experimental treatments * Active autoimmune disease requiring immunosuppressive therapy with the exception of vitiligo and autoimmune alopecia * Known active central nervous system (CNS) involvement * Subjects with a condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalent) or other immunosuppressive medications within 14 days of study drug administration. Inhaled or topical steroids, and adrenal replacement doses are permitted in absence of active autoimmune disease * Known history of any active infectious pneumonitis * Presence of acute or chronic graft-versus-host disease (GVHD) requiring active treatment unless limited to skin involvement and managed with topical steroid therapy alone * Has active cytokine release syndrome * Pregnancy or breastfeeding: Women of childbearing potential (WOCBP) must have a negative serum or urine pregnancy test (urine pregnancy test: minimum sensitivity 25 IU/L or equivalent units of human chorionic gonadotropin \[hCG\]) within 14 days of the first dose of study drug. Women must not be breastfeeding. Females of non-childbearing potential are those who are postmenopausal greater than 1 year or who have had a bilateral tubal ligation or hysterectomy. Females of childbearing potential and males who have partners of childbearing potential must agree to use 2 effective contraceptive methods during the study and for 8 months following the last dose of nivolumab