Nivolumab in Treating Patients With Relapsed or Refractory Peripheral T-cell Lymphoma

Inclusion Criteria: * Relapsed or refractory T-cell lymphoma (TCL) biopsy-proven =\< 6 months prior to registration, including the following subtypes: * Peripheral T-cell lymphoma, not otherwise specified * Anaplastic large cell lymphoma, anaplastic lymphoma kinase (ALK) negative, primary systemic type * Angioimmunoblastic T-cell lymphoma * Extranodal natural killer (NK)/T-cell lymphoma, nasal type * Adult T-cell lymphoma/leukemia (human T-lymphotropic virus 1 \[HTLV1\]+) * Blastic NK-cell lymphoma * Enteropathy-associated T-cell lymphoma * Hepatosplenic gamma delta T-cell lymphoma * Transformed mycosis fungoides * T/NK-cell lymphoma, unclassifiable * Measurable disease: subjects must have at least one lesion that is \> 15mm (1.5 cm) in the longest diameter on cross-sectional imaging and measureable in two perpendicular dimensions per computed tomography (spiral CT) or magnetic resonance imaging (MRI) * After failure of allogeneic stem cell transplant (ASCT) or after failure of frontline therapy in subjects who declined or are not ASCT candidates * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2 * White blood cell (WBC) \>= 3000/mm\^3 * Absolute neutrophil count (ANC) \>= 1500/mm\^3 * Platelet count \>= 100,000/mm\^3 * Hemoglobin \> 9.0 g/dL * Total bilirubin =\< 1.5 x upper limit of normal (ULN) unless elevation due to Gilbert's Syndrome * Aspartate transaminase (AST) =\< 2.5 x ULN * Creatinine =\< 2.0 mg/dL * Calculated creatinine clearance must be \>= 45 ml/min using the Cockcroft-Gault formula * Negative serum or urine pregnancy test done =\< 7 days prior to registration, for persons of childbearing potential only Note: Persons of child-bearing potential (POCBP) must use appropriate method(s) of contraception; POCBP should use an adequate method to avoid pregnancy for 23 weeks (30 days plus the time required for nivolumab to undergo five half-lives) after the last dose of investigational drug; men who are sexually active with POCBP must use any contraceptive method with a failure rate of less than 1% per year; men receiving nivolumab and who are sexually active with POCBP will be instructed to adhere to contraception for a period of 31 weeks after the last dose of investigational product; persons who are not of childbearing potential (ie, who are postmenopausal or surgically sterile) as well as azoospermic men do not require contraception; should a person become pregnant or suspect being pregnant while participating in this study, the person should inform the treating physician immediately * Provide written informed consent * Willing to return to enrolling institution for follow-up during the Active Monitoring phase of the study * Willing to provide tissue and blood samples for correlative research purposes Exclusion Criteria: * All primary cutaneous T-cell lymphomas * Any of the following: * Pregnant women * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens * Active, known or suspected autoimmune disease Note: subjects 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 * Use of systemic treatment with either corticosteroids (\>10 mg daily prednisone equivalents) or other immunosuppressive medications \< 14 days of registration Note: inhaled or topical steroids are permitted; \> 10 mg daily prednisone equivalents are permitted only in adrenal insufficiency in the absence of active autoimmune disease * Prohibited treatments and or therapies * Autologous stem cell transplant (ASCT) =\< 12 weeks prior to first dose of the study drug * Prior treatments (window prior to registration): * Chemotherapy =\< 2 weeks * Nitrosureas =\< 6 weeks * Therapeutic anticancer antibodies =\< 4 weeks * Radio- or toxin immunoconjugates =\< 10 weeks * Radiation therapy =\< 3 weeks * Or major surgery =\< 2 weeks * Prior treatment with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CTLA-4 antibody, or any other antibody or drug specifically targeting T-cell costimulation or immune checkpoint pathways * Prior allogeneic stem cell transplant (SCT) * Chest radiation =\< 24 weeks prior to registration * Immunocompromised patients, patients with known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS) and currently receiving antiretroviral therapy, active hepatitis B virus surface antigen (HBV sAg+), active hepatitis C (if Ab+ then PCR+) indicating acute or chronic infection * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm * Other active malignancy =\< 3 years prior to registration EXCEPTIONS: non-melanotic skin cancer or carcinoma-in-situ of the cervix NOTE: if there is a history of prior malignancy, they must not be receiving other specific treatment for their cancer * Active central nervous system (CNS) involvement or leptomeningeal involvement * History of pancreatitis