PRIMARY OBJECTIVES: I. To examine the activity and safety of adoptive therapy using ex vivo expanded memory T cells that are enriched and genetically-modified to express a cluster of differentiation (CD)19-specific, hinge optimized, CD28-costimulatory chimeric antigen receptor (CAR) as well as a truncated human epithelial growth factor receptor (EGFR) (Arm 1: CD19R(EQ)28zeta/truncated human EGFR [EGFRt]+ central memory T cells [TCM]; Arm 2: CD19R(EQ)28zeta/EGFRt+ naive and memory T cells [TN/NEM]) shortly following a lymphodepleting preparative regimen for adults with poor prognosis CD19+ acute lymphoblastic leukemia (ALL).