Testing the Combination of Nivolumab and ASTX727 for Relapsed or Refractory B-Cell Lymphoma

Inclusion Criteria: * Dose Escalation: Histologically confirmed relapsed or refractory B cell lymphoma (non-Hodgkin lymphoma \[NHL\] or Hodgkin lymphoma \[HL\]) * Dose Expansion: Patients must have histologically confirmed relapsed or refractory DLBCL or HL * Patients with DLBCL must have failed at least first line chemotherapy and must be transplant ineligible (either secondary to performance status or lack of adequate disease control or patient preference). Patients may be relapsed after autologous or allogeneic stem cell transplant (SCT), or after chimeric antigen receptor (CAR)-T cell therapy * In dose escalation patients with HL or B cell NHL other than DLBCL must have relapsed after at least 2 lines of therapy and have no other curative options left. HL patients must be brentuximab vedotin refractory or intolerant. In dose expansion, patients with classic HL must have relapsed after at least 2 lines of therapy, and had autologous stem cell transplantation (ASCT), be ineligible for ASCT, or have refused ASCT. Prior treatment with checkpoint inhibitor is allowed * Age \>= 18 years. Because no dosing or adverse event data are currently available on the use of nivolumab in combination with ASTX727 in patients \< 18 years of age, children are excluded from this study * Eastern Cooperative Oncology Group (ECOG)/Karnofsky performance status =\< 2 (Karnofsky \>= 70%) * Leukocytes \>= 1,500/mcL (unless documented bone marrow involvement in which case lower values may be allowed) * Absolute neutrophil count \>= 1,000/mcL (unless documented bone marrow involvement in which case lower values may be allowed) * Platelets \>= 75,000/mcL (unless documented bone marrow involvement in which case lower values may be allowed) * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x institutional ULN * Serum creatinine =\< 1.5 x ULN OR creatinine clearance (CrCl) \>= 50 mL/min (if using the Cockcroft-Gault formula) * Patients with a requirement for steroid treatment or other immunosuppressive treatment: Patients should be excluded if they have a condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of study drug administration. Inhaled or topical steroids and adrenal replacement doses \> 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease * Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated * Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load * Patients with treated brain metastases are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression * Patients with new or progressive brain metastases (active brain metastases) or leptomeningeal disease are eligible if the treating physician determines that immediate CNS specific treatment is not required and is unlikely to be required during the first cycle of therapy * Patients with a prior malignancy that has completed treatment and or in remission for at least 3 years, or non-melanoma skin cancer or in situ cancer are eligible for this trial. Patients with concurrent malignancy or recent treatment for a concurrent malignancy are not eligible * Patients should be New York Heart Association Functional Classification of class 2B or better * The effects of nivolumab and ASTX727 on the developing human fetus are unknown. For this reason and because DNMTi agents as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential (WOCBP) and men must agree to use highly effective contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. WOCBP should use a highly effective contraception method to avoid pregnancy during treatment with ASTX727 and for at least 6 months after the last dose of investigational drug and must agree not to donate eggs (ova, oocytes) for the purpose of reproduction for the same time period. Women of childbearing potential must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of human chorionic gonadotropin \[HCG\]) within 24 hours prior to the start of nivolumab. An extension up to 72 hours prior to the start of study treatment is permissible in situations where results cannot be obtained within the standard 24-hour window. Women must not be breastfeeding. Men who are sexually active with WOCBP must use any contraceptive method with a failure rate of less than 1% per year. Men who are sexually active with WOCBP will be instructed to adhere to highly-effective contraceptive measures of birth control and not to father a child while receiving treatment and for a period of 3 months after the last dose of investigational product. Women who are not of childbearing potential (i.e., who are postmenopausal or surgically sterile as well as azoospermic men) do not require contraception * Women of childbearing potential (WOCBP) is defined as any female who has experienced menarche and who has not undergone surgical sterilization (hysterectomy or bilateral oophorectomy) or who is not postmenopausal. Women will be considered post-menopausal if they have been amenorrheic for 12 months without an alternative medical cause. The following age-specific requirements a