Ibrutinib in Treating Minimal Residual Disease in Patients With Chronic Lymphocytic Leukemia After Front-Line Therapy

Inclusion Criteria: * Understand and voluntarily sign an informed consent form * Able to adhere to the study visit schedule and other protocol requirements including willing to provide blood, baseline bone marrow aspirate, and control deoxyribonucleic acid (DNA) samples for correlative research purposes * Diagnosis of B-cell chronic lymphocytic leukemia (B-CLL), confirmed by flow cytometry and as per the criteria outlined by the IWCLL/Hallek December 2008 * Prior frontline therapy for B-CLL must have been discontinued \>= 56 days but =\< 365 days prior to registration; NOTE: Patients on supportive care therapy due to use of specific induction regimen such as antibiotics may continue on those treatments at the discretion of the treating physician * Patient must have completed a frontline induction therapy (minimum of 2 treatment cycles); NOTE: Standard therapies/therapeutic agents are defined as those listed in the National Comprehensive Cancer Network (NCCN) guidelines for treatment of CLL; also, patients who received induction regimen as part of a clinical trial and is not necessarily mentioned in the NCCN guidelines, will also be eligible as long as the patient has completed at least 2 treatment cycles of induction regimen, achieved a clinical response (PR or CR) and is able to meet all other criteria for the study; however, patients who have previously received ibrutinib or have been randomized to ibrutinib containing arms in a clinical trial will not be eligible for this study * Patients must have a sustained clinical response (PR, nodular PR \[nPR\], complete clinical response \[CCR\], CR with incomplete marrow recovery \[CRi\], CR) with documented residual disease (\>= 1 CLL cell per 10,000 leukocytes or \>= 0.01% MRD) either in the blood, bone marrow or a lymph node \>= 3.5 cm by any available techniques * Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1 or 2 at registration * Absolute neutrophil count \>= 1000/mm\^3 * Platelet count \>= 30,000/mm\^3 * Serum creatinine =\< 1.5 x upper limit of normal (ULN) * Total bilirubin =\< 1.5 mg/dL or direct bilirubin =\< 1.0 mg/dL for patients with Gilbert's syndrome * Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) and serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 3.5 x ULN * Negative pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only Exclusion Criteria: * Any serious medical condition, laboratory abnormality, or psychiatric illness that would prevent the subject from signing the informed consent form * 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 * Use of any other experimental drug or therapy =\< 28 days prior to registration on this study; NOTE: Patients on low dose prednisone (=\< 10 mg) for treatment of conditions other than CLL are eligible * Patients who have received more than 1 prior therapy; NOTE: Prior therapy is defined as any single agent or combination regimen that is included as treatment for symptomatic CLL; treatment(s) given prior to the symptomatic phase of the disease (preventive strategy) will not be considered as prior induction therapy; 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 induction 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 who have progressive disease or relapse (as defined by the IWCLL criteria) at or any time before registration on this study * 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 are already MRD- (both in the blood and the bone marrow) after frontline therapy and have lymph nodes \< 3.5 cm * Concomitant use of warfarin or other vitamin K antagonists * Requires treatment with a strong cytochrome P450 modulators (cytochrome P450, family 3, subfamily A \[CYP3A\] inhibitor and/or CYP3A inducers) * Currently active, clinically significant hepatic impairment Child-Pugh class B or C according to the Child Pugh classification * Major surgery =\< 4 weeks prior to registration * Patients who have active infectious hepatitis * Patients with other diseases that in the opinion of the treating physician pose a higher risk for treatment with ibrutinib therapy including active human immunodeficiency virus (HIV) infection and bleeding disorders