Pembrolizumab in Combination With Chemotherapy for the Treatment of Frail Hodgkin Lymphoma Patients Ineligible for Standard Treatment

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Assent, when appropriate, will be obtained per institutional guidelines * Agreement to allow the use of archival tissue from diagnostic tumor biopsies * If unavailable, exceptions may be granted with study principal investigator (PI) approval * Meets at least one of the following criteria indicating unsuitability for conventional anthracycline-based frontline chemotherapy, as determined by the investigator: * Age ≥ 75 years * Eastern Cooperative Oncology Group (ECOG) 2-4 * Left ventricular ejection fraction (LVEF) \< 50% * Creatinine clearance \< 60 mL/min, using Cockcroft-Gault formula or equivalent * Pulmonary function impairment: forced expiratory volume in 1 second (FEV1) \< 50% and/or diffusion capacity of the lung for carbon monoxide (DLCO) \< 50% * ECOG ≤ 2 * Age ≥ 18 years * Histologically confirmed new 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 * No prior systemic treatment for classical Hodgkin lymphoma with the following exceptions: a course of systemic corticosteroids for palliation of symptoms related to the classical Hodgkin lymphoma is allowed but must be stopped by cycle 1 day 1 (C1D1) as well as prior treatment with P-G as part of this clinical trial for patients will receive P-BV-D * Measurable disease (at least one non-bone 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 * Total bilirubin ≤ 2 × upper limit of normal (ULN) or direct bilirubin ≤ 2 × ULN for patients with Gilbert's disease * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 3 x ULN * AST and ALT ≤ 3 x ULN unless there is liver involvement by lymphoma in which case AST and ALT \< 5 x ULN * For patients for whom P-BV-D therapy is planned, creatinine clearance of ≥ 30 mL/min per 24-hour urine test or the Cockcroft-Gault formula * If not receiving anticoagulants: International normalized ratio (INR) OR prothrombin (PT) ≤ 1.5 x ULN * If on anticoagulant therapy: PT must be within therapeutic range of intended use of anticoagulants * If not receiving anticoagulants: Activated partial thromboplastin time (aPTT) ≤ 1.5 x ULN * If on anticoagulant therapy: aPTT must be within therapeutic range of intended use of anticoagulants * Seronegative for hepatitis C virus (HCV), hepatitis B virus (HBV) (surface antigen negative) OR * If seropositive for HBV or HCV, nucleic acid quantitation must be performed. Viral load must be undetectable. Patients with occult or prior HBV infection (defined as negative hepatitis B virus surface antigen \[HBsAg\] and positive hepatitis B core antibody \[HBcAb\]) may be included if HBV DNA is undetectable, if they are willing to undergo DNA testing on day 1 of every cycle and every three months for at least 12 months after the last cycle of study treatment * 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 * A male participant must agree to use a contraception during the treatment period and for at least 6 months after the last dose of study treatment and refrain from donating sperm during this period * A female participant is eligible to participate if she is not pregnant, not breastfeeding, and at least one of the following conditions applies: * Not a woman of childbearing potential (WOCBP) OR * A WOCBP who agrees to follow the contraceptive guidance during the treatment period and for at least (X days/weeks \[corresponding to time needed to eliminate any study treatment(s)\] \[pembrolizumab and/or any active comparator/combination\] plus 30 days \[a menstruation cycle\] for study treatments with risk of genotoxicity) after the last dose of study treatment * TO PROCEED WITH SALVAGE TREATMENT: ECOG ≤ 2 * TO PROCEED WITH SALVAGE TREATMENT: Resolution of treatment-related adverse events (AEs) to baseline or grade 1, whichever is higher * TO PROCEED WITH SALVAGE TREATMENT: Measurable disease (at least one non-bony FDG-avid lesion ≥ 1.5 cm in long axis) * TO PROCEED WITH SALVAGE TREATMENT: Peripheral neuropathy ≤ grade 2 * TO PROCEED WITH SALVAGE TREATMENT: ANC ≥ 1,000/mm\^3 * NOTE: Growth factors are permitted * TO PROCEED WITH SALVAGE TREATMENT: Platelets ≥ 50,000/mm\^3 * NOTE: Platelet transfusions are permitted * TO PROCEED WITH SALVAGE TREATMENT: Hemoglobin ≥ 8 g/dL (no transfusion allowed within 3 days prior to screening) * TO PROCEED WITH SALVAGE TREATMENT: Total bilirubin ≤ 2 x ULN or direct bilirubin ≤ 2 x ULN for patients with Gilbert's disease * TO PROCEED WITH SALVAGE TREATMENT: AST ≤ 3 x ULN, or less then 5 x ULN for patients with liver involvement by lymphoma * TO PROCEED WITH SALVAGE TREATMENT: ALT ≤ 3 x ULN, or less then 5 x ULN for patients with liver involvement by lymphoma * TO PROCEED WITH SALVAGE TREATMENT: Creatinine clearance of ≥ 30 mL/min per 24-hour urine test or the Cockcroft-Gault formula 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, Bacille Calmette Guerin \[BCG\], oral polio vaccine, and oral typhoid) * Grade ≥ 2 peripheral neuropathy * Requirement for hemodialysis or peritoneal dialysis. Estimated glomerular filtration rate (EGFR) \> 30 for pembrolizumab + BV + dacarbazine * Known active central nervous system (CNS) involvement by lymphoma including parenchymal and/or lymphomatous meningitis * History of prior ≥ grade 3 hypersensitivity to either brentuximab vedotin or pembrolizumab * Patients with a systemic fungal, bacterial, viral, or other infection not controlled (defined as exhibiting ongoing signs/symptoms related to the infection and without improvement, despite appropriate antibiotics or other treatment) * History of another primary malignancy that has been in remission for fewer than 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 systemic 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 * Up to 7 days of 20 mg daily prednisone equivalent after C1D1 for management of lymphoma-related symptoms * History of progressive multifocal leukoencephalopathy (PML) * Active pneumonitis or interstitial lung disease * Prior solid organ or allogeneic stem cell transplantation * History of known or suspected hemophagocytic lymphohistiocytosis (HLH) * 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 (HBV) or C (HCV) infection. Patients with past HBV infection (defined as negative 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 RNA * HIV positive * 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 * 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)