A Phase 1b/2 Study to Assess the Safety and Efficacy of Subcutaneous Blinatumomab in Combination With Low Intensity Chemotherapy in Older Patients With Newly Diagnosed B-Cell Acute Lymphoblastic Leukemia

Inclusion Criteria: * Patients 60 years or older with previously untreated Ph-negative B-ALL. Patients may have received minimal prior therapy before (up to 2 cycles of previous therapy) * Patients 18 to 59 years of age with previously untreated Ph-negative B-ALL who are deemed medically unfit for intensive chemotherapy. Patients may have received minimal prior therapy (up to 2 cycles of previous therapy) * Unfit patients are defined as having at least one of the below comorbidities: 1. COG \>2 2. Severe cardiac disorder (e.g., congestive heart failure requiring treatment, ejection fraction \<50%, or chronic stable angina) 3. Severe pulmonary disorder (e.g., DLCO \<65% or FEV1 \<65%) 4. Hepatic disorder with total bilirubin 1.5 x upper limit of normal * ECOG Performance status of 0, 1, or 2. * Adequate organ function with estimated creatinine clearance of \> 50 mg/min/1.73m2, bilirubin less than or equal to 3.5 mg, 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 Class C 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 patients, between the onset of menses (as early as 8 years of age) and 55 years unless the patient presents with an applicable exclusionary factor which may be one of the following: 1. Postmenopausal (no menses in greater than or equal to 12 consecutive months). 2. History of hysterectomy or bilateral salpingo-oophorectomy. 3. Ovarian failure (Follicle Stimulating Hormone and Estradiol in menopausal range, who have received Whole Pelvic Radiation Therapy). 4. 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 is a Class C agent with 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 blinatumomab, 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 pregnancy test. WOCBP defined as not post-menopausal for 12 months or no previous surgical sterilization. * Female subjects of childbearing potential unwilling/unable to use highly effective method of contraception during treatment and for an additional 4 months after the last dose of SC blinatumomab * Prior history of therapy with SC Blinatumomab * Philadelphia positive (+) B-ALL * Known HIV-positive patients * Patients with active inflammatory or infectious hepatitis. Patients with evidence of chronic hepatitis B infection must have undetectable HBV viral load on suppressive therapy. For patients with a history of Hepatitis C, infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load. * Active and uncontrolled disease/infection as judged by the treating physician * Patients with a cardiac ejection fraction as measured by MUGA or TTE \<40% * Unable/unwilling to sign informed consent form * No other investigational therapy within the past 14 days * Symptomatic CNS disease at the time of enrollment. * 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 (\> or = grade 3) CNS events including ICANS from prior CART or other T cell engager therapies. * No other concurrent anti-leukemia therapy will be allowed, except for BCR::ABL1 tyrosine kinase inhibitors in patients with Ph-like ALL where tyrosine kinase inhibitors have been shown to be effective. * Current uncontrolled autoimmune disease or history of autoimmune disease with potential CNS involvement. * Patients with psychiatric illness/social situations that would limit compliance with study requirements.