New drug cocktail may spare hodgkin patients from stem cell transplant

Copied word for word from the study's registry entry, so the wording is the study team's rather than ours.

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Assent, when appropriate, will be obtained per institutional guidelines * Be willing to provide tissue (either from a fresh core or excisional biopsy performed as standard of care, or from archival tissue) of a biopsy that was performed after frontline systemic therapy, and prior to starting protocol therapy * If unavailable, exceptions may be granted with study principal investigator (PI) approval * Eastern Cooperative Oncology Group (ECOG) =\< 2 * Histologically confirmed diagnosis of classical Hodgkin lymphoma (excluding nodular lymphocyte predominant Hodgkin lymphoma) according to the World Health Organization (WHO) classification, with hematopathology review at the participating institution * Relapsed or refractory disease after no more than 1 line of prior therapy (not counting radiotherapy). However, a maximum of 5 patients with primary refractory disease may be enrolled in this study. Note: Patients who received BV or an anti-PD-1/PD-L1 agent as part of frontline therapy are eligible if they achieved a CMR with frontline therapy and have not relapsed within 6 months from the end of frontline therapy Relapse must have been confirmed histologically (with hematopathology review at the participating institution) * Not a candidate for ASCT, based on age, co-morbidities, or patient preference. The reason for ASCT non-candidacy must be documented in the Case Report Form and verified by the site PI * Measurable disease (at least one non-bony fludeoxyglucose F-18 \[FDG\]-avid lesion \>= 1.5 cm in long axis) * Absolute neutrophil count (ANC) \>= 1,000/mm\^3 * NOTE: Growth factor is not permitted within 7 days of ANC assessment unless cytopenia is secondary to disease involvement * Platelets \>= 50,000/mm\^3 * NOTE: Platelet transfusions are not permitted within 7 days of platelet assessment unless cytopenia is secondary to disease involvement * Hemoglobin \>= 8 g/dL (no transfusion allowed within 3 days prior to screening) * Total bilirubin =\< 1.5 x upper limit of normal (ULN) or direct bilirubin =\< 1.5 x ULN for patients with Gilbert's disease * Aspartate aminotransferase (AST) =\< 2.5 x ULN * Alanine aminotransferase (ALT) =\< 2.5 x ULN * Creatinine clearance of \>= 40 mL/min per 24 hour urine test or the Cockcroft-Gault formula * Women of childbearing potential (WOCBP): negative urine or serum pregnancy test. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Agreement by women and men of childbearing potential\* to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 5 months (women) or 7 months (men) after the last dose of protocol therapy * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only) Exclusion Criteria: * Concomitant investigational therapy * Live vaccine within 30 days prior to day 1 of protocol therapy (e.g. measles, mumps, rubella, varicella, yellow fever, rabies, bacillus Calmette-Guerin \[BCG\], oral polio vaccine, and oral typhoid) * Grade \>= 2 peripheral neuropathy * History of prior \>= grade 3 hypersensitivity to either brentuximab vedotin or nivolumab * Known active central nervous system (CNS) involvement by lymphoma, including parenchymal and/or lymphomatous meningitis * History of another primary malignancy that has not been in remission for at least 3 years, with the following exceptions: * Non-melanoma skin cancer treated with curative intent * In situ cervical cancer * If the malignancy is expected to not require any treatment for at least 2 years (this exception should be discussed with the study PI) * Condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone or equivalent) or other immunosuppressive medications within 14 days of study drug administration. Exceptions are: * Inhaled or topical steroids and * Adrenal replacement doses \> 10 mg daily prednisone equivalents in the absence of active autoimmune disease * History of progressive multifocal leukoencephalopathy (PML) * Prior diagnosis of inherited or acquired immunodeficiency * Active pneumonitis or interstitial lung disease * Active, known or suspected autoimmune disease. The following are exceptions: * Vitiligo * Psoriasis not requiring systemic treatment * Hemolytic anemia associated with the lymphoma * Type I diabetes mellitus, if adequately controlled with therapy * Thyroid disease, if adequately controlled with therapy * Conditions not expected to recur in the absence of an external trigger (such exceptions should be discussed with the study PI) * Active history of: * Hepatitis B (hepatitis B virus \[HBV\]) or C (hepatitis C virus \[HCV\]) infection. Patients with past HBV infection (defined as negative hepatitis B surface antigen \[HBsAg\] and positive hepatitis B core antibody \[HBcAb\]) are eligible if HBV DNA is undetectable. Patients who are positive for HCV antibody are eligible if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA) * Human immunodeficiency virus (HIV) infection. Subjects who have an undetectable or unquantifiable human immunodeficiency virus (HIV) viral load with CD4 \>= 200 and are on highly active antiretroviral therapy (HAART) medication are allowed. Testing to be done only in patients suspected of having infections or exposures * History of a cerebral vascular event (stroke or transient ischemic attack), unstable angina, myocardial infarction, or cardiac symptoms consistent with New York Heart Association class III-IV within 6 months prior to day 1 of protocol therapy * Pregnant or breastfeeding * Any other condition that would, in the Investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)