Daratumumab and Ibrutinib in Treating Patients With Symptomatic Chronic Lymphocytic Leukemia

Inclusion Criteria: * Diagnosis of chronic lymphocytic leukemia (CLL) meeting criteria established in the International Workshop on Chronic Lymphocytic Leukemia (IWCLL) 2008 criteria for the diagnosis and treatment of CLL * Requires therapy for symptomatic CLL in the opinion of the treating physician as defined by: * Evidence of marrow failure as manifested by the development or worsening of anemia or thrombocytopenia (not attributable to autoimmune hemolytic anemia or thrombocytopenia) * Massive (\>= 6 cm below the costal margin), progressive or symptomatic splenomegaly * Massive nodes (\>= 10 cm) or progressive or symptomatic lymphadenopathy * Constitutional symptoms, which include any of the following: * Unintentional weight loss of 10% or more within 6 months * Significant fatigue limiting activity * Fevers \>= 100.5 degrees Fahrenheit (F) for 2 weeks or more without evidence of infection * Night sweats \> 1 month without evidence of infection * No prior chemotherapy, immunotherapy, or targeted therapy for the treatment of CLL with the exception of palliative loco-regional radiotherapy and corticosteroids for symptom control * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Hemoglobin \>= 8 g/dL * Absolute neutrophil count (ANC) \>= 1000/mm\^3 * Platelets \>= 30,000/mm\^3 * Prothrombin time (PT)/partial thromboplastin time (PTT) =\< 1.5 x ULN * Total bilirubin =\<1.5 x ULN (excepting Gilbert?s syndrome) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 3 x ULN (unless due to liver involvement) * Serum creatinine \< 2.0 mg/dL OR creatinine clearance (Cockcroft) \>= 40 mL/min/1.73 m\^2 * Women of childbearing potential and men who are sexually active must be practicing a highly effective method of birth control during and after the study consistent with local regulations regarding the use of birth control methods for subjects participating in clinical trials; men must agree to not donate sperm during and after the study; for females, these restrictions apply for 1 month after the last dose of study drug; for males, these restrictions apply for 3 months after the last dose of study drug * Women of childbearing potential must have a negative serum (beta-human chorionic gonadotropin \[beta-hCG\]) or urine pregnancy test at screening; women who are pregnant or breastfeeding are ineligible for this study * Sign (or their legally-acceptable representatives must sign) an informed consent document indicating that they understand the purpose of and procedures required for the study, including biomarkers, and are willing to participate in the study * Positive hepatitis serology: * Hepatitis B virus (HBV): Patients with positive serology for hepatitis B defined as positivity for hepatitis B surface antigen (HBsAg) or hepatitis B virus core antibody (anti-HBc); patients who are positive for anti-HBc may be considered for inclusion in the study on a case-by-case basis if they are hepatitis B viral deoxyribonucleic acid (DNA) negative and are willing to undergo ongoing HBV DNA testing by real-time polymerase chain reaction (PCR); patients with positive serology may be referred to a hepatologist or gastroenterologist for appropriate monitoring and management * Patients with positive hepatitis B surface antigen (HBSAg) consistent with prior vaccination to HBV (i.e., hepatitis B virus surface antibody \[anti-HBs\]+, anti-HBc-) may participate * Patients suspected to have false positive serologic studies because of IV immunoglobulin administration are potentially eligible after negative PCR studies for viral DNA/ribonucleic acid (RNA) and discussion with the principal investigator * Hepatitis C virus (HCV): Patients with positive hepatitis C serology unless HCV RNA is confirmed negative and may be considered for inclusion in the study on a case-by-case basis (e.g., patients with negative viral load after HCV-specific treatment) Exclusion Criteria: * Patients who have had chemotherapy, immunotherapy, radiotherapy, or investigational therapy within 28 days prior to entering the study or those who have not recovered from adverse events due to agents administered more than 28 days earlier; steroids for control of disease related symptoms are permitted * Patients who are receiving any other investigational agents * History of stroke or intracranial hemorrhage within 6 months prior to randomization * Uncontrolled autoimmune hemolytic anemia or thrombocytopenia * Active Richter's transformation * Known active involvement of the central nervous system by lymphoma or leukemia * Requires anticoagulation with warfarin or equivalent vitamin K antagonists (eg, phenprocoumon); patients may be eligible if able to be taken off warfarin and started on an alternative anticoagulant * Requires chronic treatment with strong CYP3A inhibitors * Known infection with the human immunodeficiency virus (HIV) virus * Clinically significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, congestive heart failure, or myocardial infarction within 6 months of screening, or any class 3 (moderate) or class 4 (severe) cardiac disease as defined by the New York Heart Association functional classification * History of severe (defined as grade 4 and/or requiring permanent discontinuation of prior antibody therapy) allergic or anaphylactic reactions to human, humanized, chimeric, or murine monoclonal antibodies * A female patient who is pregnant or breast-feeding * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Known chronic obstructive pulmonary disease (COPD) (defined as a forced expiratory volume in 1 second \[FEV1\] \< 50% of predicted normal), persistent asthma, or a history of poorly controlled asthma within the last 2 years (controlled intermittent asthma or controlled mild persistent asthma is allowed) * History of other active malignancies other than CLL within the past 3 years prior to study entry, with the exception of adequately treated in situ carcinoma or the cervix uteri or breast, basal cell or localized squamous cell carcinoma of the skin, previous malignancy confirmed and surgically resected (or treated with other modalities) with curative intent or without relapse for \>= 2 years * Vaccination with a live vaccine \< 28 days prior to the start of treatment * Any 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 capsules, or put the study outcomes at undue risk