Daratumumab and Ibrutinib for the Treatment of Relapsed or Refractory Chronic Lymphocytic Leukemia, DIRECT Study

Inclusion Criteria: * Diagnosis of B-CLL, confirmed by flow cytometry and as per the criteria outlined by the IWCLL/Hallek December 2008 * Patients must have relapse or refractory chronic lymphocytic leukemia (CLL)/small lymphocytic lymphoma (SLL) who have received at least 1 prior anti-CLL/SLL therapy. (Note: There is no upper limit of how many lines of therapy the patient may have received previously) * Note: For the purpose of a particular therapy/regimen to be counted towards the number of prior treatments a patient must have received at least 2 cycles of the regimen e.g., a patient who change their treatment regimen after only 1 cycle (due to toxicity or any other reason) will not be considered to have "2" prior therapies * Patients on low dose prednisone (≤ 10 mg) for treatment of conditions other than CLL are eligible * Cohort 1 only: Exposed to previous bruton tyrosine kinase (BTK) inhibitor. Patients must meet one of the following criteria: * They have been previously treated with a previous BTK inhibitor and were taken off for any reason (except grade 4 toxicity definitely attributed to BTK inhibitor) as long as deemed safe by the treatment physician to receive ibrutinib * Currently on a BTK inhibitor and now have progressive disease (BTK inhibitor refractory) * Currently on BTK inhibitor and have failed to achieve either a complete remission after at least 12 cycles of treatment with BTK or have suboptimal response (\< partial response \[PR\]) after being on BTK inhibitor treatment for 6 cycles * Patients must have a measurable disease * Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1 or 2 at registration * Absolute neutrophil count \>= 1000/mm\^3 (obtained =\< 14 days prior to registration) * Hemoglobin \>= 7 g/dl (obtained =\< 14 days prior to registration) * Platelets \>= 50,000/mm\^3 (obtained =\< 14 days prior to registration) * Serum creatinine =\< 1.5 x upper limit of normal (ULN) \*OR\* creatinine clearance \> 25 ml/min) (obtained =\< 14 days prior to registration) * Total bilirubin =\< 1.5 mg/dL or direct bilirubin =\< 1.0 mg/dL for patients with Gilbert's syndrome (obtained =\< 14 days prior to registration) * Serum glutamic-oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) and serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 3 x ULN (obtained =\< 14 days prior to registration) * 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 3 months after the last dose of study drug. For males, these restrictions apply for 3 months after the last dose of study drug * Negative pregnancy test done =\< 14 days prior to registration, for persons of childbearing potential only * NOTE: If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Provide written informed consent * Willing to return to enrolling institution for follow-up (during the Active Monitoring Phase of the study) Exclusion Criteria: * Any serious medical condition, laboratory abnormality, or psychiatric illness that would prevent the subject from signing the informed consent form * Patient is known to have chronic obstructive pulmonary disease with a forced expiratory volume in 1 second (FEV1) \< 50% of predicted normal (Note: FEV1 testing is required for subjects suspected of having chronic obstructive pulmonary disease and subjects must be excluded if FEV1 \< 50% of predicted normal) * Patient is known to have moderate or severe persistent asthma within the past 2 years, or currently has uncontrolled asthma of any classification (Note: subjects who currently have controlled intermittent asthma or controlled mild persistent asthma are allowed in the study) * Since this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown, any of the following will deem the subject ineligible for the study: * Pregnant women * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception * Any condition, including the presence of laboratory abnormalities, which places the subject at unacceptable risk if he/she were to participate in the study or confounds the ability to interpret data from the study * Patients who have received no prior therapy for CLL * Patients with history of any other cancer (except non-melanoma skin cancer or carcinoma in-situ of the cervix, unless in complete remission and off therapy for that disease for \> 3 years) * Patients who have previously received daratumumab or any other anti-CD38 therapy on a clinical trial or for any other malignancy * Prior or current exposure to any of the following: * Exposure to an investigational drug (including investigational vaccine) or invasive investigational medical device for any indication within 4 weeks or 5 pharmacokinetic half-lives, whichever is longer. * Focal radiation therapy within 14 days prior to randomization with the exception of palliative radiotherapy for symptomatic management but not on measurable extramedullary plasmacytoma * Concomitant use of warfarin or other vitamin K antagonists * Requires treatment with a strong cytochrome P450 modulators (CYP3A inhibitor and/or CYP3A inducers). NOTE: A comprehensive list of inhibitors, inducers, and substrates may be found at http://medicine.iupui.edu/clinpharm/ddis/main-table/. * Major surgery =\< 4 weeks prior to registration * Patients who are: * Seropositive for human immunodeficiency virus (HIV) * Seropositive for hepatitis B (defined by a positive test for hepatitis B surface antigen \[HBsAg\]). Subjects with resolved infection (i.e., subjects who are HBsAg negative but positive for antibodies to hepatitis B core antigen \[anti-HBc\] and/or antibodies to hepatitis B surface antigen \[anti-HBs\]) must be screened using real-time polymerase chain reaction (PCR) measurement of hepatitis B virus (HBV) deoxyribonucleic acid (DNA) levels. Those who are PCR positive will be excluded. EXCEPTION: Subjects with serologic findings suggestive of HBV vaccination (anti-HBs positivity as the only serologic marker) AND a known history of prior HBV vaccination, do not need to be tested for HBV DNA by PCR * Seropositive for hepatitis C (except in the setting of a sustained virologic response \[SVR\], defined as aviremia at least 12 weeks after completion of antiviral therapy) * Clinically significant cardiac disease, including: * Myocardial infarction within 6 months before randomization, or unstable or uncontrolled disease/condition related to or affection cardiac function (e.g., unstable angina, congestive heart failure, New York Heart Association Class III-IV) * Uncontrolled cardiac arrhythmia * Screening 12-lead ECG showing a baseline corrected QT interval (QTc) \>40 msec. * Known allergies, hypersensitivity, or intolerance to monoclonal antibodies or human proteins, Dara SC or its excipients (refer to the IB) or known sensitivity to mammalian-derived products * Have received vaccination with live attenuated vaccines within 4 weeks of first study agent administration * Patients with inability to swallow capsules or tablets, or disease significantly affecting gastrointestinal function and/or inhibiting small intestine absorption (malabsorption syndrome, resection of the small bowel, poorly controlled inflammatory bowel disease, etc.)