Ibrutinib in Treating Patients With Relapsed or Refractory B-cell Acute Lymphoblastic Leukemia

Inclusion Criteria: * Relapsed or refractory B-ALL due to receive salvage 1, 2, 3, 4, 5, or 6; half of the patients, i.e. 5 out of the first 10 patients, and 5 out of 10 patients thereafter, need to be in earlier line of salvage therapy, defined as 1st, 2nd, or 3rd line of salvage therapy; Philadelphia chromosome-positive (Ph+) B-ALL patients must have failed treatment with at least 1 second generation tyrosine kinase inhibitor; patients in salvage 1 with late relapse should be deemed poor candidates for reinduction with initial therapy; patients with ALL of T cell origin (T-ALL) can not be treated * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Total bilirubin =\< 1.5 × upper limit of normal (ULN) (unless Gilbert's syndrome or disease infiltration of the liver is present) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.0 × institutional ULN * Creatinine clearance (Cockcroft-Gault) greater than or equal to 30 mL/min or estimated (est) glomerular filtration rate (GFR) greater than or equal to 30 mL/min/1.73 m\^2 * For any surgery or invasive procedure requiring sutures or staples for closure, ibrutinib should be held at least 7 days prior to the intervention and should be held at least 7 days after the procedure, and restarted at the discretion of the investigator when the surgical site is reasonably healed without serosanguineous drainage or the need for drainage tubes * Bone marrow involvement with \>= 5% lymphoblasts, peripheral blast count less than 5,000 per uL * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; 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; female patients need a negative serum or urine pregnancy test within 14 days of study start (applies only if patient is of childbearing potential); non-childbearing is defined as \>= 1 year postmenopausal or surgically sterilized; men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of ibrutinib administration * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who receive other chemotherapy; patients must have been off previous therapy for \>= 2 weeks and must have recovered from clinically significant toxicity (to grade 1 or less) of all previous therapy prior to enrollment (consent signing) with the following exceptions: steroids, hydroxyurea, oral mercaptopurine, methotrexate, vincristine (including prophylactic intrathecal medication), thioguanine, and tyrosine kinase inhibitors are permitted within 2 weeks of randomization as maintenance or to reduce the peripheral blood blast counts; during ibrutinib therapy, only steroids and hydroxyurea are permitted to reduce peripheral blood blast counts; patients who have had chemotherapy or radiotherapy within 2 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 2 weeks earlier * Patients who are receiving any other investigational agents * Active central nervous system (CNS) leukemia, as defined by unequivocal morphologic evidence of lymphoblasts in the cerebrospinal fluid (CSF), use of CNS-directed local treatment for active disease within the prior 28 days, symptomatic CNS leukemia (i.e., cranial nerve palsies or other significant neurologic dysfunction) within 28 days; prophylactic intrathecal medication is not a reason for exclusion; patients with known brain metastases should be excluded from this clinical trial * History of allergic reactions attributed to compounds of similar chemical or biologic composition to ibrutinib * Concomitant use of drugs that strongly inhibit cytochrome P450, family 3, subfamily A, polypeptide 4/5 (CYP3A4/5) * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection or an infection requiring systemic antibiotics, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant and breastfeeding women are excluded from this study; breastfeeding should be discontinued if the mother is treated with ibrutinib * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are eligible, unless the patient's cluster of differentiation (CD)4 count is below the institutional lower limit of normal, or the patient is taking prohibited CYP3A4/5 strong inhibitors or inducers * Uncontrolled autoimmune hemolytic anemia or idiopathic thrombocytopenic purpura (ITP) resulting in (or as evidenced by) declining platelet or hemoglobin (Hgb) levels within the 4 weeks prior to first dose of study drug * Presence of transfusion-dependent thrombocytopenia * Prior exposure to ibrutinib * 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 * Burkitt's or mixed lineage leukemia, T cell ALL * Isolated extramedullary relapse (i.e., testicular or CNS) * Patients with a cardiac ejection fraction (as measured by either multi gated acquisition scan \[MUGA\] or echocardiogram) \< 45% are excluded; 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 infarction within 6 months prior to first dose with study drug * Unable to swallow capsules, or disease significantly affecting gastrointestinal function and/or inhibiting small intestine absorption, such as malabsorption syndrome, resection of the small bowel, or poorly controlled inflammatory bowel disease affecting the small intestine * Serologic status reflecting active hepatitis B or C infection; patients that are hepatitis B core antibody positive but antigen negative will need a negative polymerase chain reaction (PCR) prior to enrollment; (hepatitis B antigen or PCR positive patients will be excluded;) (this may not be a necessary exclusion for an ibrutinib monotherapy protocol) * History of stroke or intracranial hemorrhage within 6 months prior to enrollment * Current life-threatening illness, medical condition, or organ system dysfunction which, in the Investigator's opinion, could compromise the patient's safety, or put the study at risk; any other severe concurrent disease, or have a history of serious organ dysfunction or disease involving the heart, kidney, liver or other organ system that may place the subject at undue risk to undergo therapy with ibrutinib * Any serious medical condition, laboratory abnormality, or psychiatric illness that places the subject at unacceptable risk if he/she were to participate in the study * Received anticoagulation therapy with warfarin or equivalent vitamin K antagonists within the last 28 days * Evidence of clinically significant bleeding diathesis or coagulopathy * Major surgical procedure, open biopsy, or significant traumatic injury, within 28 days prior to day 1, anticipation of need for major surgical procedure during the course of the study; (minor surgical procedures, fine needle aspirations or core biopsies within 7 days prior to day 1; bone marrow aspiration +/- biopsy is allowed) * Prior allogeneic stem cell transplant in previous 3 months