Donor Peripheral Stem Cell Transplant in Treating Patients With Hematolymphoid Malignancies

This phase 1 trial studies the side effects and the best dose of donor CD8+ memory T-cells in treating patients with hematolymphoid malignancies. Giving low dose of chemotherapy before a donor peripheral blood stem cell transplant helps stop the growth of cancer cells. It may also stop the patient\'s immune system from rejecting the donor\'s stem cells. The donated stem cells may replace the patient\'s immune cells and help destroy any remaining cancer cells (graft-versus-cancer effects). Giving an infusion of the donor\'s T cells (donor lymphocyte infusion) after the transplant may help increase this effect