Recurrent B Lymphoblastic Lymphoma

This phase I trial tests the safety and side effects of B-cell activating factor receptor (BAFFR) chimeric antigen receptor (CAR) T cells and how well they work in treating patients with B-cell acute lymphoblastic leukemia (B-ALL) and B-cell lymphoblastic lymphoma that has come back after a period of improvement (relapsed) or that has not responded to previous treatment (refractory). CAR T-cell therapy, such as BAFFR-CAR T cells, is a type of treatment in which a patient's T cells (a type of immune system cell) are changed in the laboratory so they will attack cancer cells. T cells are taken from a patient's blood. Then the gene for a special receptor that binds to a certain protein on the patient's cancer cells is added to the T cells in the laboratory. The special receptor is called a CAR. Large numbers of the CAR T cells are grown in the laboratory and given to the patient by infusion for treatment of certain cancers. Giving BAFFR-CAR T cells may be safe, tolerable and/or effective in treating patients with relapsed or refractory B-cell ALL and B-cell lymphoblastic lymphoma.