• 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