CD19-Car T Cell Therapy for the Treatment of Older Adults With Acute Lymphoblastic Leukemia in First Remission

Inclusion Criteria: * Documented informed consent of the participant * Agreement to allow the use of archival tissue from diagnostic tumor biopsies * If unavailable, exceptions may be granted with Study Principal Investigator (PI) approval * Note: For research participants who do not speak English, a short form consent may be used with a City of Hope (COH) certified interpreter/translator to proceed with screening and leukapheresis, while the request for a translated full consent is processed. However, the research participant is allowed to proceed with lymphodepletion and T cell infusion only after the translated full consent form is signed * Age: \>= 55 years * Eastern Cooperative Oncology Group (ECOG) \< 2 / Karnofsky Performance Status (KPS) \>= 70 * Ability to read and understand English for Questionnaires * Histologically confirmed CD19+ ALL at the time of diagnosis * In morphological first complete remission regardless of minimal residual disease (MRD) status * No immediate plan for transplant * Remission after induction +/- reinduction therapy * Fully recovered from the acute toxic effects (except alopecia) to =\< Grade 1 to prior anti-cancer therapy * Total bilirubin =\< 1.5 X upper limit of normal (ULN) (unless has Gilbert's disease) * Aspartate aminotransferase (AST) =\< 3 x ULN * Alanine transaminase (ALT) =\< 3 x ULN * Creatinine clearance of \>= 60 mL/min per 24 hour urine test or the Cockcroft-Gault formula * Left ventricular ejection fraction (LVEF) \>= 50% * Note: To be performed within 28 days prior to start of protocol therapy * Oxygen (O2) saturation \> 92% on room air. * Note: To be performed within 28 days prior to start of protocol therapy * Seronegative for human immunodeficiency virus (HIV) (quantitative polymerase chain reaction \[qPCR\]), hepatitis C virus (HCV), active hepatitis B virus (HBV) (Surface Antigen Negative), and syphilis (rapid plasma reagin \[RPR\]) * If positive, hepatitis C ribonucleic acid (RNA) quantitation must be performed OR * If seropositive for HIV, HCV or HBV, nucleic acid quantitation must be performed. Viral load must be undetectable * Meets other institutional and federal requirements for infectious disease titer requirements * Note Infectious disease testing to be performed within 28 days prior to start of protocol therapy * Women of childbearing potential (WOCBP): negative urine or serum pregnancy test * 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 6 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: * History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agent(s) * Research participant with known CNS-2 or CNS-3 involvement that is refractory to intrathecal chemotherapy and/or cranio-spinal radiation. Research participants with a history of central nervous system (CNS) disease that has been effectively treated to complete remission (\<5 WBC/mm3 and no blasts in cerebrospinal fluid \[CSF\]) will be eligible * Autoimmune disease or active graft versus host disease (GVHD) requiring systemic immunosuppressant therapy * Class III/IV cardiovascular disability according to the New York Heart Association (NYHA) Classification * History of other malignancies, except for malignancy surgically resected (or treated with other modalities) with curative intent, basal cell carcinoma of the skin or localized squamous cell carcinoma of the skin; non-muscle invasive bladder cancer; malignancy treated with curative intent with no known active disease present for \>= 2 years * Clinically significant uncontrolled illness * Active systemic uncontrolled infection requiring antibiotics * Known history of HIV or hepatitis B or hepatitis C infection * Subjects who are hepatitis B core antibody (anti-HBc) positive and who are surface antigen negative will need to have a negative polymerase chain reaction (PCR) result. Those who are hepatitis B surface antigen (HbsAg) positive or hepatitis B PCR positive will be excluded * Subjects who are hepatitis B core antibody positive (or have a known history of HBV infection) should be monitored quarterly with a quantitative PCR test for HBV deoxyribonucleic acid (DNA). HBV monitoring should last until 12 months after last dose of study drug. Any subject with a rising viral load (above lower limit of detection) should discontinue study drug and have antiviral therapy instituted and a consultation with a physician with expertise in managing hepatitis B. Subjects who are core Ab positive at study enrollment are strongly recommended to start Entecavir before start and until completion of study treatment * Subjects who are hepatitis C antibody positive will need to have a negative PCR result. Those who are hepatitis C PCR positive will be excluded * Females only: Pregnant or breastfeeding * Concurrent use of systemic steroids or chronic use of immunosuppressant medications. Recent or current use of inhaled steroids is not exclusionary. Physiologic replacement of steroids (prednisone =\< 7.5 mg /day or equivalent) is allowed * 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)