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)