Nivolumab, Ifosfamide, Carboplatin, and Etoposide as Second-Line Therapy in Treating Patients With Refractory or Relapsed HL

Inclusion Criteria: * Patients must have histologically documented or cytologically confirmed Hodgkin lymphoma; confirmation must include CD30 expression * Patients must be either refractory to or relapsed after only induction therapy; patients who do not achieve CR after induction therapy are considered primary refractory and are allowed to enter study * \> 40 kg * Absolute neutrophil count (ANC) \>= 1500/uL; filgrastim can be given before and during treatment to achieve target ANC \>= 1500 uL * Platelet (Plt) \>= 75,000/uL * Hemoglobin \>= 8.5 g/dl * Platelet transfusion and packed red blood cell transfusion can also be given prior to the start of treatment and treatment to achieve a target plt \>= 75,000/uL and hemoglobin of \>= 8.5 g/dl, provided that patients have not received growth factors for at least 14 days prior to entering trial * Patients must have measurable disease \> 1.5 cm evidenced by computed tomography (CT) scan of the neck/chest/abdomen/pelvis or CT/positron emission tomography (PET) scans * Life expectancy of greater than 3 months * Eastern Cooperative Oncology Group (ECOG) of 0-2 * Documented informed consent/assent of the participant or legally responsible guardian * Diffusion capacity of the lung for carbon monoxide (DLCO) \>= 60% * Total bilirubin with 1.5 x the upper limit of normal (ULN) institutional limits; patients with elevation of unconjugated bilirubin alone, as in Gilbert's disease, are eligible * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 3.0 x the institutional upper limit of normal (unless demonstrated Hodgkin lymphoma involvement of the liver); estimated creatinine clearance \>= 30 ml/min (Cockcroft-Gault) and/or 24 urine analysis as needed * For patients with Hodgkin lymphoma (HL) involvement of the liver, AST/ALT \< 5.0 x institutional ULN; total bilirubin within 3.0 x institutional ULN; (although patients with HL involvement of the liver are frequently excluded from trials, their liver function tests often improve after treatment; the studies that led to nivolumab approval did not reveal any increased signals of liver toxicities attributed to nivolumab) * Prothrombin time (PT)/international normalized ration (INR) \< 1.5 x ULN and partial thromboplastin time (PTT) (activated \[a\]PTT) \< 1.5 x ULN * Female subject is either post-menopausal, surgically sterilized, or willing to use and acceptable method of birth control (i.e., a hormonal contraceptive, intra-uterine device, diaphragm with spermicide, condom with spermicide, or abstinence) for the duration of the study; women of childbearing potential (WOCBP) must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 24 hours prior to the start of nivolumab * Men who are sexually active with WOCBP must use any contraceptive method with a failure rate of less than 1% per year; men receiving nivolumab and who are sexually active with WOCBP will be instructed to adhere to contraception for a period of 31 weeks 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 * All participants will undergo standard written informed consent procedures as dictated by the City of Hope Human Research Protections Office prior to performing any screening procedures that are not part of standard-of-care; informed consent will be obtained by the principal investigator, collaborating investigators, or other Institutional Review Board (IRB) designated personnel who will meet the training requirements established by the IRB; with the support of research personnel, he/she will explain the nature, duration, purpose of the study, potential risks, alternatives and potential benefits, and all other information contained in the informed consent document; in addition, they will review the experimental subject's bill of rights and the Health Insurance Portability and Accountability Act (HIPAA) research authorization form; prospective research participants will be informed that they may withdraw from the study at any time and for any reason without prejudice; prospective research participants will be afforded sufficient time to consider whether or not to participate in the research * Patient must be either refractory to or relapsed after 1 line of therapy; prior radiation therapy is allowed * INCLUSION CRITERIA FOR COHORT B: * B symptoms at relapse * Extranodal disease at relapse * Primary refractory disease * Relapsed \< 1 year after completion of frontline therapy * Have received brentuximab vedotin as initial therapy Exclusion Criteria: * Prior exposure to PD-1 or PD-L1 inhibitors is not allowed * Must not have had second line chemotherapy for Hodgkin lymphoma * Active autoimmune diseases requiring systemic treatments * Vaccinated with live, attenuated vaccine within 4 weeks of first dose of study drug * Any life-threatening illness, medical condition, or organ system dysfunction that, in the investigator's opinion, could compromise the subject's safety or put the study outcomes at undue risk * Unwilling or unable to participate in all required study evaluations and procedures * Unable to understand the purpose and risks of the study and to provide a signed and dated informed consent for (ICF) and authorization to use protected health information (in accordance with national and local subject privacy regulations) * Patients should not have any uncontrolled illness including ongoing or active infection * Patients may not be receiving any other investigational agents, or concurrent biological therapy, chemotherapy, or radiation therapy * Patients must not have received prior chemotherapy or radiation for =\< 3 weeks before study enrollment, or those who have not recovered from the adverse events due to agents administered more than 3 weeks earlier are excluded * Myocardial infarction within 6 months prior to enrollment or New York Heart Association (NYHA) class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities; prior study entry, any electrocardiogram (ECG) abnormality at screening has to be documented by the investigator as not medically relevant * Significant screening electrocardiogram (ECG) abnormalities including, but not limited to, left bundle branch block, 2nd degree atrioventricular (AV) block type II, 3rd degree block, or corrected QT interval (QTc) \>= 470 msec; subjects with a cardiac pacemaker who have a QTc interval of \>= 470 msec may be eligible if these findings are considered not clinically significant as documented via a cardiology evaluation * DLCO \< 60%; the clinical studies in support of accelerated approval for nivolumab in chronic (c)HL after failure of ASCT required DLCO \> 60%; certain HL induction regimens have the potential for pulmonary toxicity, and nivolumab carries the potential of pneumonitis or other pulmonary toxicities * Diagnosed or treated for another malignancy within 3 years of enrollment, with the exception of complete resection of basal cell carcinoma or squamous cell carcinoma of the skin, an in situ malignancy, or low-risk prostate cancer after curative therapy * Patients with active central nervous system (CNS) disease or history of brain metastases are excluded from study * 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 * Pregnant women are excluded from this study because of the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk of adverse events in nursing infants secondary to treatment of the mother, breastfeeding should be discontinued * Recent infection requiring systemic treatment that was completed =\< 14 days before the first dose of study drug * Known history of human immunodeficiency virus (HIV), hepatitis C virus (HCV) or hepatitis B virus (HBV) infection; subjects who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment, those who are PCR positive will be excluded; subjects who have an undetectable HIV viral load with CD4 \>= 300 and are on highly active antiretroviral therapy (HAART) medication are allowed; previously treated hepatitis C patients are also allowed; as there is potential for hepatic toxicity with nivolumab or nivolumab/ipilimumab combinations, drugs with a predisposition to hepatoxicity should be used with caution in patients treated with nivolumab-containing regimen * History of allergy or adverse drug reaction to study components