Can a Patient's own immune cells be trained to cure leukemia?

Copied word for word from the study's registry entry, so the wording is the study team's rather than ours.

Inclusion Criteria: Patients must be ≥12 months of age and \<27 years of age at the time of study enrollment. Must be ≥10kg Confirmed CD19+ leukemia recurrence defined as ≥0.01% disease in the marrow or isolated extramedullary disease following allogeneic HCT. \[N.B. Study closed to enrollment of leukemia subjects\] OR No prior history of allogeneic HCT (one of the following) * 2nd or greater relapse, with or without extramedullary disease (isolated extramedullary disease is eligible) * 1st marrow relapse at end of 1st month of re-induction with marrow having ≥0.01% blast disease, with or without extramedullary disease * Primary Refractory as defined as having M2 or M3 marrow after induction * Subject has indication for HCT but has been deemed ineligible OR CD19+ Non-Hodgkin Lymphoma (NHL) refractory or relapsed with no known curative therapies available \[N.B. Study remains open to enrollment of lymphoma subjects\] Patients with CNS involvement are eligible provided that they are asymptomatic and in the opinion of the study PI have a reasonable expectation that disease burden can be controlled in the interval between enrollment and T cell infusion. Patients that have a significant neurologic deterioration will be not be eligible for T cell infusion until alternate therapies result in neurological stabilization. Patients must have a Lansky performance status score of ≥50 or a Karnofsky score of ≥ 50 for patients ≥16 years of age. Life Expectancy of \>8 weeks Patients must be free from active GVHD and off immunosuppressive GVHD therapy for 4 weeks prior to enrollment. Recovered from acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy It must be at least 7 days since last chemotherapy was administered (this does not include intrathecal chemotherapy or maintenance chemotherapy) No systemic corticosteroids (unless physiologic replacement dosing) within 7 days of enrollment. No prior genetically modified cell therapy that is still detectable or virotherapy allowed. * Normal serum creatinine based on age/gender * Total bilirubin \</3x ULN OR conjugated bilirubin \</2mg/dl * ALT \</5X ULN * SF of \>28% by ECHO or EF \>50% by MUGA * ALC of \>/= 100 cells/ul * Pulse ox \>/= 90% on room air Patient must have documented negative HIV antigen and antibody, Hepatitis B surface antigen, and Hepatitis C antibody within 3 months prior to enrollment. For patient with positive Hepatitis C Ab, negative PCR testing must be documented in order to be eligible. Patients must NOT have active clinically significant CNS dysfunction (including but not limited to such as uncontrolled seizure disorder, paresis, aphasia, cerebrovascular ischemia/hemorrhage, severe brain injuries, dementia, cerebellar disease, organic brain syndrome, psychosis, coordination or movement disorder) Must agree to highly effective contraception during and for 12 months after T cell infusion. Patients must be able to tolerate apheresis procedure, including placement of temporary apheresis line if required. Patients must NOT have an active malignancy other than CD19+ leukemia. Patients must NOT have an active severe infection defined as: * A positive blood culture within 48 hours of study enrollment * A fever above 38.2 C AND clinical signs of infection within 48 hours of study enrollment Patients must NOT have any concurrent medical condition that, in the opinion of the PI or designee, would prevent the patient from undergoing protocol-based therapy. Patients with a primary immunodeficiency/ bone marrow failure syndrome are excluded from this trial. Research participant or parent/legal guardian must agree to participate in long-term follow-up for up to 15 years, if they are enrolled in the study and receive T-cell infusion.