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

PRIMARY OBJECTIVES:

I. To determine the feasibility of purifying allogeneic CD8+ memory T-cells suitable for clinical application and to determine the safety and maximum tolerated dose (MTD) of these cells in patients with recurrent or refractory hematolymphoid malignancies following allogeneic hematopoietic cell transplant (HCT).

SECONDARY OBJECTIVES:

I. To determine disease response, time to disease progression, event-free survival, and overall survival following treatment with allogeneic CD8+ memory T-cells.

II. To assess donor specific chimerism before and at designated time points after treatment with allogeneic CD8+ memory T-cells.

OUTLINE: This is a dose-escalation study.

Patients undergo CD8+ memory T-cell infusion over 10 to 20 minutes.

Inclusion Criteria:

• Patients must have undergone a human leukocyte antigen (HLA) matched (sibling) allogeneic HCT for a hematologic or lymphoid malignancy other than chronic myelogenous leukemia (CML) who have recurrent or persistent disease and are otherwise eligible for donor leukocyte infusions CML patients with persistent disease after receiving donor lymphocyte infusion of at least 1x10^8cells/kg will be eligible for CD8+ memory T cell infusion
• Patients must have no evidence of active graft-versus-host disease and must be on a stable immunosuppressive regimen without a change in drugs dosage in the 4 weeks prior to the planned CD8+ memory T cell infusion
• Patients must not have any active infections
• Patients must have a performance status of > 70% on the Karnofsky scale
• Serum creatinine of < 2 mg/dl or creatinine clearance of > 50 cc/min
• Bilirubin of < 3 mg/dl Transaminases < 3 times the upper limit of normal
• Patients must have negative antibody serology for the human immunodeficiency virus (HIV1 and 2) and hepatitis C virus and negative test for hepatitis B surface antigen

DONOR:

• Donors must be an HLA matched sibling
• Donors must be 18-75 years of age, inclusive
• Donors must be in a state of general good health
• Donors must have a white blood cell count > 3.5 x 10^9/liter DONOR: Platelets > 150 x 10^9/liter
• Donors: Hematocrit > 35%
• Donors must be capable of undergoing leukapheresis
• Donors must not be seropositive for HIV 1 and 2, Hepatitis B surface antigen, Hepatitis B core antibody, Hepatitis C antibody, human T-lymphotropic virus (HTLV) antibody, cytomegalovirus (CMV) immunoglobulin (Ig)M, or Rapid Plasma Reagin (RPR) (Treponema)
• Female donors must not be pregnant or lactating

Exclusion Criteria:

• Diagnosis of CML except patients who have failed prior donor leukocyte infusion with a minimum cell dose of 1x10^8 cells/kg
• Patients who have been diagnosed with a second cancer (except carcinoma in situ of the cervix and basal cell carcinoma of the skin) which is currently active or has been treated within three years prior to screening