Cellular Immunotherapy in Treating Patients With High-Risk Acute Lymphoblastic Leukemia

Inclusion Criteria: * City of Hope (COH) pathology review confirms that research participant's diagnostic material is consistent with history of ALL with history of recurrence/progression/minimal residual disease (MRD) following prior therapy; additionally, CD19 positivity must be documented in a pathology report; however, it is not a requirement that the CD19 testing be performed by a COH pathologist; patients in second complete remission (CR2) or higher with history of CD19+ ALL on previous bone marrow biopsy are also eligible for the study * Research participants with confirmed 1st or higher relapse of disease by morphology, cytogenetics or molecular, or research participants with refractory or residual disease * Minimal residual disease (MRD) will be defined in this protocol by presence of malignant cells at 0.01% or more by flow cytometry or polymerase chain reaction (PCR) analysis at the completion of initial remission induction therapy * Participants with central nervous system (CNS) involvement by leukemia (CNS2 and CNS3) may be considered eligible after discussions with the study team. * Karnofsky performance status (KPS) of \>= 70% * Life expectancy \>= 16 weeks at time of enrollment * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control or abstinence) prior to study entry and for six months following duration of study participation; should a woman become pregnant or suspect that she is pregn…