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