Nivolumab and Brentuximab Vedotin in Treating Older Patients With Untreated Hodgkin Lymphoma

Inclusion Criteria: * Classical Hodgkin lymphoma determined by local hematopathology review * One of the following: * Age \>= 60 years * Age \< 60 years but unsuitable for standard chemotherapy because of a cardiac ejection fraction of \< 50%, a pulmonary diffusion capacity \< 80%, or a creatinine clearance \>= 30 and \< 60 mL/min, or refused standard chemotherapy despite efforts to convince them otherwise * Requirement for systemic chemotherapy: all stages except IA (not bulky disease), if involved field is considered radiotherapy (RT) curative * Previously untreated with either chemotherapy, radiation therapy or either brentuximab vedotin or nivolumab, or another check point inhibitor * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, or 2 * Absolute neutrophil count (ANC) \>= 1500/mm\^3, unless secondary to bone marrow involvement; obtained =\< 7 days prior to registration * Leukocytes \>= 3,000/mm\^3, obtained =\< 7 days prior to registration * Platelet count \>= 100,000/mm\^3, obtained =\< 7 days prior to registration * Hemoglobin \> 9.0 g/dL - unless determined by treating physician to be disease related, obtained =\< 7 days prior to registration * Total bilirubin =\< 1.5 x upper limit of normal (ULN), obtained =\< 7 days prior to registration * Aspartate aminotransferase (aspartate transaminase \[AST\]) =\< 2.5 x ULN, obtained =\< 7 days prior to registration * Alanine aminotransferase (alanine transaminase \[ALT\]) =\< 2.5 x ULN, obtained …