Genetically Engineered Cells (BAFFR-CAR T Cells) for the Treatment of Relapsed or Refractory B-cell Acute Lymphoblastic Leukemia and B-cell Lymphoblastic Lymphoma

PRIMARY OBJECTIVE: I. Assess the safety of administering autologous BAFFR-targeting CAR T cells (BAFFR\[EQ\]BBζ/EGFRt T cells) (also known as \[aka\], BAFFR-CAR T cells). SECONDARY OBJECTIVES: I. Evaluate the ability of BAFFR-CAR T cells to mediate clinical response in participants with B-ALL. II. Evaluate the level of residual disease in participants who achieve remission after BAFFR-CAR T cell treatment. III. Evaluate the duration of B cell aplasia as a surrogate for BAFFR-CAR T cell activity. IV. Evaluate the rate and severity of graft-versus-host disease (GVHD) in recipients of prior allogeneic hematopoietic stem cell transplantation (allogeneic hematopoietic stem cell transplantation \[allo-HCT\]). V. Evaluate progression-free survival (PFS) and overall survival (OS). EXPLORATORY OBJECTIVES: I. Measure expansion and persistence of BAFFR-CAR T cells in the peripheral blood (PB), bone marrow (BM), and cerebrospinal fluid (CSF), when available, and explore the correlation with BAFFR-CAR T cell efficacy. II. Measure BAFF-R expression on leukemic cells, as well as other disease markers, before and after BAFFR-CAR T cell treatment and explore association with response and relapse, when feasible. III. Measure cytokine levels in PB and CSF, when available, and explore association with response. OUTLINE: Patients undergo leukapheresis and may receive bridging therapy per treating physician discretion. Patients then receive lymphodepletion therapy with cyclophosphamide intravenously (IV) and fludarabine IV on days -5 to -3 and BAFFR-CAR T cells IV over 10-15 minutes on day 0. Patients also undergo blood sample collection, bone marrow aspiration and biopsy, chest x-ray, and positron emission tomography (PET)/computed tomography (CT) or CT throughout the study. Additionally, patients may also undergo liver ultrasonographic elastography at screening at discretion of investigator and brain magnetic resonance imaging (MRI) or CT, CSF specimen collection, and echocardiography (ECHO) or multigated acquisition scan (MUGA) throughout the study After completion of study treatment, patients are followed up within 18-24 hours, at least every 2 days for 14 days, at 14, 21, 28, 60, and 100 days, at 4, 6, 7, and 12 months, then yearly for up to a total of 15 years.