Donor Cord Blood T-Cell Infusion After Stem Cell Transplant in Treating Patients With Relapsed Hematological Malignancies

This phase I trial studies the side effects and best dose of donor cord blood T-cells after stem cell transplant in treating patients with relapsed hematological malignancies. After umbilical cord blood transplant, stem cells are collected from the donor's cord blood and stored. The stem cells are then returned to the patient to replace the blood-forming cells that were destroyed by treatment. Removing the T cells and treating them in the laboratory before infusing them in the patient may also help boost the patient's immune system.