PCI-32765 (Ibrutinib) in Treating Patients With Relapsed or Refractory Chronic Lymphocytic Leukemia, Small Lymphocytic Lymphoma, or B-cell Prolymphocytic Leukemia

Inclusion Criteria:

* Confirmed diagnosis of relapsed/refractory CLL/SLL who require treatment and have failed at least one prior therapy.
* Patients must have available results of interphase cytogenetics CLL fluorescent in situ hybridization (FISH) panel; the cytogenetic analysis must be done prior to starting therapy but after any recent therapy
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2
* Life expectancy greater than 2 months
* Bilirubin =\< 1.5 X the institutional upper limit of normal unless due to Gilbert's disease or disease related to Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) =\< 2.5 X the institutional upper limit of normal unless disease related
* Creatinine =\< 1.5 X the institutional upper limit of normal unless disease related
* Absolute neutrophil count (ANC) \>= 0.75 X 10\^9/L
* Platelet count \>= 30 X 10\^9/L
* Agree to use contraception during the study and for 30 days after the last dose of study drug if sexually active and able to bear children
* Ability to understand and the willingness to sign a written informed consent document
* Patients with uncontrolled or active infection requiring antibiotic therapy; patients with controlled infections who are receiving extended antibiotics or prophylactic therapy are not excluded

Exclusion Criteria:

* Patients who have had chemotherapy, radiotherapy or immunotherapy within 4 weeks prior to the first dose of study drug (corticosteroids for disease-related symptoms allowed but doses equivalent to \> 20 mg prednisone orally per day require 1 week washout before study drug administration or steroid dose must be equal to =\< 20 mg prednisone orally daily)
* Patients who have not recovered from adverse events of \>= grade 3 toxicity due to agents administered more than 4 weeks ago
* Receiving any other investigational agents
* Previously randomized to any PCI-32765 clinical trial
* Known secondary malignancy that limits survival to less than two years
* Patients with malabsorption syndrome, disease significantly affecting gastrointestinal function, or resection of the stomach or small bowel or ulcerative colitis, symptomatic inflammatory bowel disease, or partial or complete bowel obstruction
* Patients requiring anti-coagulation with warfarin or other Vitamin K antagonists or heparin products including low molecular weight heparin (LMWH)
* Currently active, clinically significant hepatic impairment Child-Pugh class B or C according to the Child Pugh classification
* Patients requiring treatment with a strong cytochrome P450 3A4/5 (CYP3A4/5) and/or cytochrome P450 2D6 (CYP2D6) inhibitor
* Patients with 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 PCI-32765 PO, 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
* Active central nervous system (CNS) involvement by lymphoma
* Pregnant or women who are breastfeeding