Phase 2 Study to Assess the Safety and Efficacy of Subcutaneous Blinatumomab in Patients With Measurable Residual Disease Positive B-cell Acute Lymphoblastic Leukemia

Inclusion Criteria * Participants of age ≥18 years with documented B-cell ALL with recurrent or persistent MRD (at a sensitivity of 10-6) while in morphological remission (Includes Ph-, Ph+ and Ph-like). * ECOG Performance status of 0, 1, or 2. * Adequate organ function with creatinine less than or equal to 1.6 mg/dl, bilirubin less than or equal to 3.5 mg/dl and ALT and/or AST less than or equal to 5 times institutional upper limit of normal. * The effects of blinatumomab on the developing human fetus are unknown. For this reason and because bispecific T-cell engager agents as well as other therapeutic agents used in this trial are known to be teratogenic, 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. (Refer to Pregnancy Assessment Policy MD Anderson Institutional Policy # CLN1114). This includes all female Participants, between the onset of menses (as early as 8 years of age) and 55 years unless the Participant presents with an applicable exclusionary factor which may be one of the following: * Postmenopausal (no menses in greater than or equal to 12 consecutive months). * History of hysterectomy or bilateral salpingo-oophorectomy. * Ovarian failure (Follicle Stimulating Hormone and Estradiol in menopausal range, who have received Whole Pelvic Radiation Therapy). * History of bilateral tubal ligation or another surgical sterilization procedure. * Approved methods of birth control are as follows: Hormonal contraception (i.e. birth control pills, injection, implant, transdermal patch, vaginal ring), Intrauterine device (IUD), Tubal Ligation or hysterectomy, Subject/Partner post vasectomy, Implantable or injectable contraceptives, and condoms plus spermicide. Not engaging in sexual activity for the total duration of the trial and the drug washout period is an acceptable practice; however, periodic abstinence, the rhythm method, and the withdrawal method are not acceptable methods of birth control. 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. * 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 blinatumomab administration. * Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria * Pregnant women are excluded from this study because Blinatumomab, a bispecific T-cell engager agent has the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with blinatumomb, breastfeeding should be discontinued if the mother is treated with blinatumomab. These potential risks may also apply to other agents used in this study. * Women of child-bearing potential (WOCBP) must have negative urine or serum pregnancy test within 1 week of study therapy initiation. WOCBP defined as not post-menopausal for 12 months or no previous surgical sterilization. * Female subjects of childbearing potential unwilling to use 1 highly effective method of contraception during treatment and for an additional 4 months after the last dose of protocol specified therapy. * Symptomatic CNS leukemia * History or presence of clinically relevant CNS pathology or event such as epilepsy, childhood or adult seizure, paresis, aphasia, stroke, severe brain injuries, dementia, Parkinson's disease, cerebellar disease, organic brain syndrome, psychosis or severe (≥ grade 3) CNS events including ICANS from prior CART or other T cell engager therapies. * Isolated extramedullary B-cell ALL * Current autoimmune disease or history of autoimmune disease with potential CNS involvement. * Active acute or chronic graft versus host disease post-allogeneic HSCT requiring systemic treatment with immunosuppressive medication. * Prior history of therapy with SQ blinatumomab for R/R B-cell as part of a clinical trial (but not prior therapy with IV blinatumomab) * Known hypersensitivity to blinatumomab or to any component of the product formulation * Uncontrolled HIV, HBV, HCV infections * Active and uncontrolled disease/infection as judged by the treating physician. * Unable or unwilling to sign the consent form. * No other investigational therapy within the past 14 days * Participants with psychiatric illness/social situations that would limit compliance with study requirements.