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 sc…