Ibrutinib and Nivolumab in Treating Patients With Relapsed or Refractory Classical Hodgkin Lymphoma

Inclusion Criteria: * Patients with histologically confirmed classical HL that is relapsed or refractory after at least one prior therapy are eligible * Patients with lymphocyte predominant Hodgkin's are eligible * Prior treatments: patients must have had at least one prior therapy * Patients with previous autologous transplant are permitted * Patients who are eligible and willing to undergo autologous transplant should not be enrolled on this trial * Prior allogeneic transplant is NOT permitted * Prior treatment with Bruton's tyrosine kinase (BTK) inhibitors is NOT permitted * Prior treatment with nivolumab is permitted * Presence of radiographically measurable disease (defined as the presence of a \>= 1.0 cm lesion, as measured in the longest dimension by computed tomography \[CT\] scan or positron emission tomography \[PET\]/CT scan or magnetic resonance imaging \[MRI\] scan) * Absolute neutrophil count (ANC) \> 1000/uL * Platelets \> 75,000/uL * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2 x upper limit of normal (ULN) * Total bilirubin =\< 1.5 x ULN * Creatinine =\< 2.0 mg/dl * Eastern Cooperative Oncology Group (ECOG) performance status of =\< 2 * Patients with human immunodeficiency virus (HIV) are not permitted to enroll * Patients with history of hepatitis B or C infection are not permitted to enroll; to enroll patients must have no evidence of hepatitis B or C surface antigen (Ag) and negative hepatitis B core antibody (Ab); patients previously immunized for hepatitis B who are hepatitis B surface Ab positive, but surface Ag and core Ab negative are eligible * Non-pregnant and non-nursing; pregnant and nursing patients may not be enrolled; women and men of reproductive potential must agree to use acceptable forms of contraception during the study * Willing and able to participate in all required evaluations and procedures in this study protocol including swallowing capsules without difficulty * Ability to understand the purpose and risks of the study and provide signed and dated informed consent and authorization to use protected health information (in accordance with national and local subject privacy regulations) Exclusion Criteria: * Prior malignancy, except for adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, or other cancer from which the subject has been disease free for \>= 2 years or which will not limit survival to \< 2 years * A life-threatening illness, medical condition or organ system dysfunction which, in the investigator's opinion, could compromise the subject's safety, interfere with the absorption or metabolism of ibrutinib, or put the study outcomes at undue risk * Significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, congestive heart failure, or myocardial infarction within 6 months of screening, or any class 3 or 4 cardiac disease as defined by the New York Heart Association Functional Classification * Malabsorption syndrome, disease significantly affecting gastrointestinal function, or resection of the stomach or small bowel, symptomatic inflammatory bowel disease, partial or complete bowel obstruction, or gastric restrictions and bariatric surgery, such as gastric bypass * Central nervous system (CNS) involvement by lymphoma * Has a diagnosis of immunosuppression or is receiving ongoing immunosuppressive therapy, including systemic or enteric corticosteroids for treatment of lymphoid cancer or other conditions * Note: subjects may use topical or inhaled corticosteroids or low-dose steroids (=\< 20 mg of prednisone or equivalent per day) as therapy for comorbid conditions; during study participation, subjects may also receive systemic or enteric corticosteroids as needed for treatment-related toxicities * Has an active autoimmune disease or history of autoimmune disease such as hepatitis, hypophysitis, nephritis, hyperthyroidism or hypothyroidism, interstitial lung disease, colitis * Requires or is currently receiving anticoagulation with warfarin or equivalent vitamin K antagonists (eg, phenprocoumon) within 28 days of first dose of study drug * Requires treatment with a strong cytochrome P450 (CYP) 3A inhibitor * Currently active, clinically significant hepatic impairment Child-Pugh class B or C according to the Child Pugh classification * Major surgery within 4 weeks before first dose of study drug * History of stroke or intracranial hemorrhage within 6 months before the first dose of study drug