Nivolumab in Treating Patients With HTLV-Associated T-Cell Leukemia/Lymphoma

Inclusion Criteria: * Patients with any stage of pathologically confirmed cluster of differentiation (CD)3+ acute, lymphoma, chronic, or smoldering subtypes of ATLL * Documentation of HTLV infection (enzyme linked immunosorbent assay \[ELISA\]) in individual with confirmation of HTLV-1 infection (by immunoblot or polymerase chain reaction \[PCR\]) or a consistent clinical picture (including two of the following: 1) CD4+ leukemia or lymphoma, 2) hypercalcemia, and/or 3) Japanese, Caribbean or South American birthplace) * Patients with acute or lymphoma forms must have received at least one cycle of combination chemotherapy (with or without mogamulizumab) or interferon (with or without zidovudine and/or arsenic); individuals with chronic or smoldering acute T-cell lymphoma (ATL) are not required to have had prior treatment or could have received any number of previous courses of therapy * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 (Karnofsky \>= 60%) * Life expectancy \> 12 weeks * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin within normal institutional limits * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal * Creatinine within normal institutional limits OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; or abstinence) prior to study entry and for the duration of study participation; women should continue birth control for 23 weeks after stopping nivolumab, and men should continue birth control for 31 weeks after stopping nivolumab; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately; men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 31 weeks after completion of nivolumab administration * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier * Patients who are receiving any other investigational agents * History of allergic reactions attributed to compounds of similar chemical or biologic composition to nivolumab * Prior allogeneic transplantation * 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 * Any condition requiring \> 10 mg/d prednisone equivalents * Current or prior HTLV-1 associated inflammatory diseases, including but not limited to myelopathy, uveitis, arthropathy, pneumonitis, or a Sjogren's disease-like disorder * Prior treatment with anti-PD-1, anti-programmed death-ligand (PD-L)1, anti-PD-L2 antibody * Grade 2 or greater toxicity from prior therapy * Grade 2 or greater diarrhea * Patients with active autoimmune disease or history of autoimmune disease that might recur, which may affect vital organ function or require immune suppressive treatment including systemic corticosteroids, should be excluded; these include but are not limited to patients with a history of immune related neurologic disease, multiple sclerosis, autoimmune (demyelinating) neuropathy, Guillain-Barre syndrome, myasthenia gravis; systemic autoimmune disease such as systemic lupus erythematosus (SLE), connective tissue diseases, scleroderma, inflammatory bowel disease (IBD), Crohn's, ulcerative colitis, hepatitis; and patients with a history of toxic epidermal necrolysis (TEN), Stevens-Johnson syndrome, or phospholipid syndrome should be excluded; patients with vitiligo, endocrine deficiencies including thyroiditis managed with replacement hormones including physiologic corticosteroids are eligible; patients with rheumatoid arthritis and other arthropathies (other than HTLV-associated arthropathy), and psoriasis controlled with topical medication and patients with positive serology, such as antinuclear antibodies (ANA), anti-thyroid antibodies should be evaluated for the presence of target organ involvement and potential need for systemic treatment but should otherwise be eligible; 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) * Patients who have had evidence of active or acute diverticulitis, intra-abdominal abscess, gastrointestinal (GI) obstruction and abdominal carcinomatosis which are known risk factors for bowel perforation should be evaluated for the potential need for additional treatment before coming on study * Patients who have hepatitis C (both reactive anti-hepatitis C virus \[HCV\] antibody and detectable HCV RNA) and hepatitis B (hepatitis B surface antigen \[HBsAg\] positive and anti-hepatitis B core \[HBc\]-total positive), may be enrolled, provided their total bilirubin: =\< 1.5 x institutional upper limit of normal (ULN) AST (SGOT)/ALT (SGPT): =\< 2.5 x institutional upper limit of normal * Patients with concurrent human immunodeficiency virus (HIV) infection may be enrolled if compliant with 3 or more drug anti-retroviral regimen and virus load less than 50 copies/ml and CD4 count greater than 250 cells/ml, and no concurrent opportunistic infection or other malignancy * Any other prior malignancy from which the patient has been disease free for less than 3 years, with the exception of adequately treated and cured basal or squamous cell skin cancer, superficial bladder cancer, carcinoma in situ of any site or any other cancer * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with nivolumab