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 creatini…