Ibrutinib and Blinatumomab in Treating Patients With Relapsed or Refractory B Acute Lymphoblastic Leukemia

Inclusion Criteria: * Pathologically confirmed diagnosis of relapsed or refractory B-cell acute lymphoblastic leukemia/lymphoma with measurable bone marrow lymphoblasts or biopsy-proven extramedullary site measurable by computed tomography (CT) or positron emission tomography (PET)/CT imaging; Philadelphia chromosome-positive (Ph+) B-ALL patients must have failed treatment with at least one second generation tyrosine kinase inhibitor; prior allo-HCT is allowed * No hematologic parameters for inclusion; transfusion-dependent patients are eligible and platelet counts should be maintained greater than 10,000/mm\^3 throughout cycles 1 and 2 * Bilirubin less than or equal to 1.5 x upper limit of normal (ULN) (unless bilirubin rise is due to Gilbert's syndrome or B-ALL or non-hepatic origin) * Serum aspartate transaminase (aspartate aminotransferase \[AST\]) or alanine transaminase (alanine aminotransferase \[ALT\]) less than or equal to 3 x ULN (unless due to B-ALL) * Estimated creatinine clearance greater than or equal to 30 ml/min (Cockcroft-Gault) or serum creatinine less than or equal to 2 x ULN * Prothrombin time (PT)/international normalized ratio (INR) =\< 1.5 x ULN and partial thromboplastin time (PTT) (activated partial thromboplastin time \[aPTT\]) =\< 1.5 x ULN (unless B-ALL related) * Karnofsky performance status (KPS) performance status of 60% or greater * Ability to understand and willingness to sign an informed consent form * Ability to adhere to the study visit schedule and other protocol requirements * Female subjects who are of non-reproductive potential (i.e., post-menopausal by history - no menses for \>= 1 year; OR history of hysterectomy; OR history of bilateral tubal ligation; OR history of bilateral oophorectomy); female subjects of childbearing potential must have a negative serum or urine pregnancy test within 72 hours prior to the first study drug administration * Male and female subjects who agree to use both a highly effective methods of birth control (e.g., condoms, implants, injectables, combined oral contraceptives, some intrauterine devices \[IUDs\], complete abstinence, or sterilized partner) and a barrier method (e.g. condoms, vaginal ring, sponge, etc) during the period of therapy and for 90 days after the last dose of study drug * Eligibility of patients receiving any medications or substances known to affect or with the potential to affect the activity or pharmacokinetics of ibrutinib or blinatumomab will be determined following review of their case by the investigator Exclusion Criteria: * Diagnosis of T acute lymphoblastic leukemia (T-ALL) or Burkitt's leukemia/lymphoma * Patients with current evidence of active central nervous system (CNS) leukemia * History of treatment with ibrutinib or blinatumomab * Investigational therapy, chemotherapy, immunotherapy, radiotherapy, or systemic graft versus host disease (GVHD) therapy within two weeks or five half-lives (whichever is shorter); steroids, hydroxyurea and/or leukapheresis are allowed to control blast count prior to the first dose of study drug * Prior allo-HCT less than three months from the time of enrollment * Any active acute GVHD or chronic GVHD greater than grade 1 * History of allergic reactions attributed to compounds of similar chemical or biologic composition to ibrutinib and blinatumomab or other agents used in this study * Vaccinated with live, attenuated vaccines within 4 weeks of first dose of study drug * Recent culture-documented infection requiring intravenous antimicrobials that was completed =\< 7 days before the first dose of study drug or any uncontrolled active systemic infection; fever of unknown origin is not an exclusion criterion, as this may be disease-related * Unresolved toxicities from prior anti-cancer therapy, defined as having not resolved to Common Terminology Criteria for Adverse Event (CTCAE, version \[v\]4.03), grade =\< 2, or to the levels dictated in the inclusion/exclusion criteria with the exception of alopecia * Known bleeding disorders (e.g., von Willebrand's disease) or hemophilia * History of stroke or intracranial hemorrhage within 6 months prior to enrollment * Active infection with human immunodeficiency virus (HIV), hepatitis C virus (HCV) or hepatitis B virus (HBV); subjects who are positive for hepatitis B core antibody, hepatitis B surface antigen, or hepatitis C antibody must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded; subjects with HIV must have a CD4 count at or above the institutional lower limit of normal and not taking prohibited CYP3A strong inhibitors * Major surgery within 4 weeks of first dose of study drug * Any life-threatening illness, medical condition, or organ system dysfunction, including but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, active autoimmune disorder, or psychiatric illness/social situations that, in the investigator's opinion, could compromise the subject's safety or put the study outcomes at undue risk; currently active, clinically significant cardiovascular disease, such as uncontrolled arrhythmia or class 3 or 4 congestive heart failure as defined by the New York Heart Association Functional Classification; or a history of myocardial infarction, unstable angina, or acute coronary syndrome within 6 months prior to enrollment * History of other malignancies, except for malignancy surgically resected (or treated with other modalities) with curative intent, adequately treated in situ carcinoma of the breast or cervix uteri, basal cell carcinoma of the skin or localized squamous cell carcinoma of the skin; malignancy treated with curative intent with no known active disease present for \>= 3 years * Concomitant use of warfarin or other Vitamin K antagonists * Subjects who received a strong cytochrome P 450 3A (CYP3A) inhibitor within 7 days prior to the first dose of ibrutinib or subjects who require continuous treatment with a strong CYP3A inhibitor * Currently active, clinically significant hepatic impairment Child-Pugh class B or C according to the Child Pugh classification * Breastfeeding or pregnant * Participation in clinical trials with other investigational agents not included in this trial throughout the duration of this trial * Unwilling or unable to participate in all required study evaluations and procedures or unable to understand the purpose and risks of the study and to provide a signed and dated informed consent form (ICF) and authorization to use protected health information (in accordance with national and local subject privacy regulations)