Ibrutinib in Treating Relapsed or Refractory B-Cell Non-Hodgkin Lymphoma in Patients With HIV Infection

Inclusion Criteria: * Known HIV infection and histologically confirmed B-cell non-Hodgkin lymphoma or B-cell lymphoproliferative disease as follows, as defined by the World Health Organization classification: * Active B-cell non-Hodgkin lymphoma (cluster of differentiation \[CD\]20 positive or negative), chronic lymphocytic leukemia (CLL) or small lymphocytic lymphoma (SLL), or multiple myeloma that has relapsed, progressed, or been refractory to at least one regimen * Note: Patients with CLL, SLL, or mantle cell lymphoma (MCL) may only be enrolled in Stratum C * At least 14 days between ibrutinib initiation and last cancer therapy; any number of prior cancer therapies is permitted; patients otherwise fit for blood or marrow transplantation (BMT) should receive second-line chemotherapy before considering enrollment * Serologic documentation of HIV infection at any time prior to study entry, as evidenced by positive enzyme-linked immunosorbent assay (ELISA), positive Western blot, or any other federally approved licensed HIV test; alternatively, this documentation may include a record that another physician has documented that the participant has HIV infection based on prior ELISA and Western blot, or other approved diagnostic tests * Participants must be on a stable antiretroviral regimen per current International Acquired Immunodeficiency Syndrome (AIDS) Society guidelines as follows, with no intention of changing the regimen within 8 weeks after ibrutinib initiation: * Choice of regimen: The specific antiretroviral agents are at physician discretion, and the use of investigational agents currently available on an expanded-access basis is allowed; use of experimental antiretroviral agents or those containing zidovudine (including Combivir and Trizivir) is prohibited * Patients with mantle cell lymphoma, CLL, or SLL must be on non-cytochrome P450, family 3, subfamily A, polypeptide 4 (CYPA3A4) modulating antiretroviral agents (Stratum C) to be eligible for this study * Patients may be switched to non-conflicting regimens in order to participate * Stability of regimen: With the exception of patients on zidovudine-based ART, any changes in antiretroviral regimen must be made at least 4 weeks prior to ibrutinib initiation; patients taking zidovudine-based ART must change to a non-zidovudine-based regimen at least 2 weeks prior to ibrutinib initiation; changes to ART therapy during the study may be made if medically necessary (e.g. toxicity, treatment failure) * Eastern Cooperative Oncology Group (ECOG) performance status 0, 1 or 2 (Karnofsky \>= 60%) * Life expectancy \>= 2 months * Absolute CD4+ lymphocyte count: \>= 75 cells/uL * Absolute neutrophil count \>= 750 cells/uL * Platelets \>= 50,000 cells/uL, or \>= 30,000/uL if bone marrow is involved by malignancy * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.0 x institutional upper limit of normal (ULN), or =\< 5.0 x ULN if attributable to malignancy * Total bilirubin =\< 2.0 x ULN, unless elevated bilirubin is attributable to Gilbert's syndrome or to HIV medications (e.g., indinavir, tenofovir, atazanavir) * Creatinine clearance (CrCl) \>= 40 mL/min (modified Cockcroft-Gault) * All subjects must be screened for hepatitis B and C infection; subjects must either have no history of hepatitis B or C, or must meet the following criteria in order to e eligible: * Hepatitis B: Subjects infected with hepatitis B must receive anti-hepatitis B therapy; per Infectious Diseases Society of America (IDSA) and American Association for the Study of Liver Diseases (AASLD) guidelines, subjects that show no immunity, defined by the lack of hepatitis B surface antibody, and show evidence of chronic infection (i.e. hepatitis B surface antigen positive \[HBsAg+\], hepatitis B core antibody positive \[HB core AB +\], hepatitis B surface antibody negative \[HBsAB-\]) must be on anti-hepatitis B therapy throughout the study in order to be eligible; the exact hepatitis B therapy is at the discretion of the infection disease specialist or investigator; all patients diagnosed with hepatitis B must also meet the liver function test criteria listed above and have no evidence of cirrhosis; however, all patients who present with acute hepatitis B, or who show normal transaminases but are HBsAg+ and immunoglobulin M positive (IgM+) for hepatitis B core antigen, are ineligible * Hepatitis C: Subjects, who are hepatitis C antibody positive, with or without a positive hepatitis C ribonucleic acid (RNA) level, must meet the liver function test criteria listed above and have no evidence of cirrhosis; patients diagnosed with hepatitis C less than 6 months before enrollment will be considered to have acute hepatitis C and will be ineligible unless the hepatitis C viral load is undetectable * Must in the opinion of the investigator be capable of complying with this protocol * Patients may not begin protocol therapy within 7 days of major surgery or within 3 days of minor surgery * Willingness of sexually active subjects to use adequate contraception; both men and women of child-bearing potential treated or enrolled on this study must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) before study entry, for the duration of study participation, and 4 months after completion of ibrutinib; men who only have sex with other men do not need to use contraception specifically for this study; (should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately) * Ability to understand and willingness to sign a written informed consent document Exclusion Criteria: * Prior exposure to ibrutinib * Receipt of any investigational agents within 14 days before the first dose of ibrutinib * Failure to recover to baseline or Common Terminology Criteria for Adverse Events (CTCAE) =\< grade 2 from clinically significant toxicities due to prior cancer therapies or to any investigational agents * Active central nervous system involvement by malignancy; central nervous system disease that has been treated into remission is permitted; a chart note of the clinician's impression of lack of central nervous system (CNS) involvement is acceptable * Patients who require concomitant treatment with CYP3A4/5 strong inhibitors or inducers OTHER than antiretroviral therapies for HIV * As part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter product * A prednisone equivalent of \< 20 mg daily is permitted in patients requiring chronic use; larger doses must be discontinued \>= 7 days prior to ibrutinib initiation and are prohibited during study treatment * Anticoagulation with warfarin or equivalent vitamin K antagonists within 28 days prior to starting ibrutinib and throughout the study * Significant or uncontrolled intercurrent condition including, but not limited to: * Infection other than HIV, hepatitis B, or hepatitis C that is symptomatic or requires systemic treatment * Opportunistic infection within 60 days prior to enrollment * Currently active clinically significant cardiovascular disease such as uncontrolled arrhythmia, congestive heart failure, any class 3 or 4 cardiac disease as defined by the New York Heart Association Functional Classification, or history of myocardial infection within 6 months prior to enrollment * History of stroke or intracranial hemorrhage within 6 months prior to enrollment * History of class B or class C cirrhosis, per the modified Child-Pugh classification * Psychiatric illness that would limit compliance * Inability to swallow capsules whole, or disease significantly affecting gastrointestinal function and/or inhibiting small intestine absorption, such as malabsorption syndrome, small bowel resection, or poorly controlled inflammatory bowel disease affecting the small intestine * History of prior malignancy, with the exception of the following: * Malignancy treated with curative intent and with no evidence of active disease present for more than 3 years prior to screening and felt to be at low risk for recurrence by treating physician * Adequately treated non-melanomatous skin cancer or lentigo maligna melanoma without current evidence of disease * Adequately treated cervical carcinoma in situ without current evidence of disease * Skin-limited Kaposi sarcoma that has not required systemic treatment within 6 months prior to study enrollment * History of allergic reactions attributed to compounds of similar chemical or biologic composition to ibrutinib * Pregnancy or breastfeeding; a pregnancy test must be performed within 7 days prior to ibrutinib initiation in women of childbearing potential; pregnant women are excluded; breastfeeding must be discontinued