Recombinant Erwinia Asparaginase and Venetoclax in Combination With Blinatumomab for the Treatment of Relapsed or Refractory CD19 Positive B-cell Acute Lymphoblastic Leukemia

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Age between 12 and 55 * Eastern Cooperative Oncology Group (ECOG) ≤ 2 or Karnofsky performance status (KPS) ≥ 70 * Patients with relapsed or refractory (R/R) CD19 positive (+) B-cell acute lymphoblastic leukemia (B-ALL) according to World Health Organization (WHO) criteria * Greater than or equal to 5% blasts in the bone marrow * White blood cell count less than 25 x 10\^9/L prior to initiation of venetoclax. (within 14 days prior to day 1 of protocol therapy) Cytoreduction with hydroxyurea, steroid or a single dose of cyclophosphamide chemotherapy prior to treatment may be required * Total bilirubin ≤ 1.5 x upper limit of normal (ULN) (within 14 days prior to day 1 of protocol therapy) (unless has Gilbert's disease or underlying leukemia, ≤ 3 x ULN) * Prothrombin time (PT) ≤ 1.5 ULN (within 14 days prior to day 1 of protocol therapy) * Partial thromboplastin time (PTT) ≤ 1.5 ULN (within 14 days prior to day 1 of protocol therapy) * Aspartate aminotransferase (AST) ≤ 2.5 x ULN (within 14 days prior to day 1 of protocol therapy) (Unless it is related to underlying leukemia, then AST ≤ 5 x ULN) * Alanine aminotransferase (ALT) ≤ 2.5 x ULN (within 14 days prior to day 1 of protocol therapy) (Unless it is related to underlying leukemia, then ALT ≤ 5 x ULN) * Creatinine clearance of ≥ 60 mL/min per 24 hour urine test or the Cockcroft-Gault formula (within 14 days prior to day 1 of protocol therapy) * Left ventricular ejection fraction (LVEF) ≥ 50% (within 14 days prior to day 1 of protocol therapy) * Note: Echocardiogram to be performed within 42 days prior to day 1 of protocol therapy * Women of childbearing potential (WOCBP): Negative urine or serum pregnancy test (within 14 days prior to day 1 of protocol therapy) * If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Agreement by females and males of childbearing potential to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 3 months after the last dose of protocol therapy * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only). Exclusion Criteria: * Allogeneic hematopoietic cell transplantation (HCT) within 8 weeks prior to the start of protocol-specific therapy. Subjects must be off all immunosuppression for ≥ 2 weeks * Cancer chemotherapy within 2 weeks before the start of protocol-specified therapy with the exception of: intrathecal chemotherapy and/or low-dose maintenance therapy (e.g. vina alkaloids, mercaptopurine, methotrexate, or hydroxyurea etc) * Strong and moderate CYP3A4 inducers and strong CYP3A inhibitors within 7 days prior to day 1 of protocol therapy * Foods/supplements that are strong inhibitors or strong or moderate inducers of CYP3A (such as grapefruit, Seville oranges, starfruit and St. John's wort) within 3 days prior to initiation of and during study treatment * Immunotherapy (e.g. rituximab) within 4 weeks before the start of protocol-specified therapy. Prior failed CD19-directed therapy such as prior blinatumomab or CD19-directed chimeric antigen receptor (CAR)-T cells will be allowed if treatment ended \> 4 weeks prior to start of protocol-specific therapy and there is demonstrated continued CD19+ expression * Must not have received or planning to receive live vaccine while being on study or 2 weeks before and after completion of treatment * Patients with any prior intolerance leading to discontinuation of pegylated (PEG)-asparaginase due to grade 3 or more pancreatitis or central nervous system thrombosis requiring anticoagulant treatment attributed to the PEG-asparaginase * Active ALL in the central nervous system (CNS): Presence of \> 5 white blood cells (WBC) per cubic millimeter in the cerebrospinal fluid (CSF) with lymphoblasts present (confirmed by CSF analysis) and/or clinical signs of CNS leukemia. If CSF leukemia is present, subjects will need to receive intrathecal chemotherapy and have documented negative CSF prior to enrollment * Active acute or chronic graft versus host disease requiring systemic treatment with immunosuppressive medication * History of intracranial thrombosis or history of recurrent thrombosis or grade 3 and greater pulmonary embolism (except for catheter-related thrombosis) * Participants with history of grade ≥ 3 pancreatitis * History of alcohol overuse if deemed relevant in investigator's opinion * Known hypersensitivity to blinatumomab/ recombinant Erwinia asparaginase or to any component of the product formulation, otherwise prior treatment with single agent blinatumomab is allowed * Uncontrolled active infection * Clinically significant uncontrolled illness or cirrhosis * Other active malignancy (except superficial skin cancers squamous cell carcinoma \[SCC\]/basal cell carcinoma \[BCC\], early-stage malignancies ductal carcinoma in-situ \[DCIS\] status post \[s/p\] excision or elevated prostate specific antigen \[PSA\]) * Females only: Pregnant or breastfeeding * Any other condition that would, in the investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)