Brentuximab Vedotin, Cyclosporine, and Verapamil Hydrochloride in Treating Patients With Relapsed or Refractory Hodgkin Lymphoma

Inclusion Criteria:

* All patients and/or their parents or legal guardians must have the ability to understand and the willingness to sign a written informed consent
* Voluntary written informed consent must be obtained before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care
* Weight over 40 kg
* Life expectancy of greater than 3 months
* Patients must have histologically documented or cytologically confirmed Hodgkin lymphoma
* Patient must have measurable disease \> 1.5 cm evidenced by computed tomography (CT) of the neck/chest/abdomen (abd)/pelvis or CT/positron emission tomography (PET) scans
* Be willing to provide tissue from a fresh core or excisional biopsy (performed as standard of care) of a tumor lesion prior to starting study therapy or from archival tissue of a biopsy that was performed after the most recent systemic therapy. Exception can be granted by the principal investigator (PI) if a biopsy is not feasible and/or safe
* Patients must be either refractory to or relapsed after at least 1 line of therapy
* Prior brentuximab vedotin is allowed; expansion cohort is defined as:

  * Expansion cohort: BV refractory: Patient who had prior exposure to BV, and either - achieved a best response of stable disease (SD) or progressive disease (PD) or - achieved a best response of complete response (CR)/PR but developed PD while on active BV treatment
* Eastern Cooperative Oncology Group (ECOG) performance score of 0-2
* Prior chemotherapy or radiation therapy is allowed if received \>= 3 weeks before study enrollment
* Prior hematopoietic transplantation is allowed (autologous and/or allogeneic)
* Absolute neutrophil count (ANC) \>= 1,000/mm\^3; filgrastim can be given prior to enrollment to achieve target ANC \>= 1000/uL (to be performed within 10 business days prior to day 1)
* Platelets \>= 50,000/mm\^3; NOTE: platelet transfusion and packet red blood cell transfusion can be given prior to enrollment to achieve a target platelet (Plt) \>= 50,000/uL and hemoglobin of \>= 8.5 g/dL (to be performed within 10 business days prior to day 1)
* Hemoglobin \>= 8.5 g/dL (to be performed within 10 business days prior to day 1)
* Total bilirubin within 1.5 x the upper limit of normal institutional limits; patients with elevation of unconjugated bilirubin alone, as in Gilbert's disease, are eligible (to be performed within 10 business days prior to day 1)
* Aspartate aminotransferase (AST) =\< 3 x upper limit of normal (ULN) unless demonstrated Hodgkin lymphoma involvement of the liver (to be performed within 10 business days prior to day 1)
* Alanine aminotransferase (ALT) =\< 3 x ULN unless demonstrated Hodgkin lymphoma involvement of the liver (to be performed within 10 business days prior to day 1)
* Creatinine clearance of \>= 50 mL/min per the Cockcroft-Gault formula and/or 24 hour (hr) urine analysis as needed (to be performed within 10 business days prior to day 1)
* If not receiving anticoagulants: international normalization ratio (INR) OR prothrombin (PT) =\< 1.5 x ULN; if on anticoagulant therapy: PT must be within therapeutic range of intended use of anticoagulants (to be performed within 10 business days prior to day 1)
* 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 (to be performed within 10 business days prior to day 1)
* Female of childbearing potential: 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 (to be performed within 10 business days prior to day 1)
* In patients who are to receive VRP, base systolic blood pressure (SBP) \> 110; diastolic blood pressure (DBP) \> 60 and baseline heart rate \> 60 (to be performed within 10 business days prior to day 1)
* Cardiac function (12 lead-electrocardiogram \[ECG\] versus \[vs\] non 12 led ECG) shows no underlying arrhythmia or heart blocks (for VRP only) (to be performed within 10 business days prior to day 1)
* Female subjects must be either post-menopausal, surgically sterilized, or willing to use an acceptable method of birth control (i.e. a hormonal contraceptive, intra-uterine deice, diaphragm with spermicide, condom with spermicide, or abstinence) beginning prior to study entry, for the duration of the study, and for six months duration of study participation; should a woman become pregnant or suspect that she is pregnant while participating on the trial, she should inform her treating physician immediately
* Male subjects must agree to use an acceptable method of contraception beginning prior to study entry, for the duration of the study, and for six months following duration of study participation

Exclusion Criteria:

* Patients who are hematopoietic stem cell transplant candidates are excluded
* Vaccinated with live, attenuated vaccines within 4 weeks of enrollment
* Patients may be on steroids prior to initiation of treatment, provided that, by cycle 1 day 1, steroid use is tapered down to less than or equal to 20 mg/day of prednisone
* Patients may not be receiving any other investigational agents, or concurrent biological therapy, chemotherapy, or radiation therapy
* Active graft versus host disease (GVHD) or on immunosuppressive medication of GVHD
* Recent infection requiring intravenous anti-infective treatment that was completed =\< 14 days before enrollment
* Unresolved toxicities from prior anticancer therapy, defined as having resolved to Common Terminology Criteria for Adverse Events (CTCAE, version 4.03), grade 0 or 1, with the exception of alopecia
* Baseline grade II peripheral neuropathy
* Hypersensitivity to BV or history of allergic reaction attributed to compounds of similar chemical or biologic composition of BV
* Unable to swallow capsules or malabsorption syndrome, disease significantly affecting gastrointestinal function, or resection of the stomach or small bowel, symptomatic inflammatory bowel disease or ulcerative colitis, or partial or complete bowel obstruction
* Patients should not have any uncontrolled illness including ongoing or active infection
* 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
* 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 to study entry, any 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
* 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
* Known active human immunodeficiency virus (HIV) or hepatitis C virus (HCV) or hepatitis B virus (HBV) infection; subjects who have an undetectable HIV viral load with CD4 \>= 200 and are on highly active antiretroviral therapy (HAART) medication are allowed; 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; patients who have had hepatitis C but have finished treatment and are PCR negative will be allowed; (testing to be done only in patients suspected of having infections or exposures)
* Pregnant women are excluded from this study because of the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother, breastfeeding should be discontinued
* 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)
* Unable to understand the purpose and risks of the study and to provide a signed and dated informed consent form (ICF) and authorization to use protected health information (in accordance with national and local subject privacy regulations)