CD8+ Memory T-Cells as Consolidative Therapy After Donor Non-myeloablative Hematopoietic Cell Transplant in Treating Patients With Leukemia or Lymphoma

This phase 2 trial studies how well cluster of differentiation 8 (CD8)+ memory T-cells work as a consolidative therapy following a donor non-myeloablative hematopoietic cell transplant in treating patients with leukemia or lymphoma. Giving total lymphoid irradiation and anti-thymocyte globulin before a donor hematopoietic cell transplant helps stop the growth of cells in the bone marrow, including normal blood-forming cells (stem cells) and cancer cells. When the healthy stem cells from a donor are infused into the patient they may help the patient's bone marrow make stem cells, red blood cells, white blood cells, and platelets. Sometimes the transplanted cells from a donor can make an immune response against the body's normal cells (called graft-versus-host disease). Giving cyclosporine and mycophenolate mofetil after the transplant may stop this from happening. Once the donated stem cells begin working, the patient's immune system may see the remaining cancer cells as not belonging in the patient's body and destroy them. Giving an infusion of the donor's white blood cells, such as CD8+ memory T-cells, may boost this effect and may be an effective treatment to kill any cancer cells that may be left in the body (consolidative therapy).

Participants undergo total lymphoid irradiation (TLI) on Days -11 to -7 and Days -4 to -1 and receive anti-thymocyte globulin (ATG) per standard institutional practice on Days -11 to -7. Patients also receive oral cyclosporine daily starting on Day -3, and will continue for at least 6 months post-transplant. Patients undergo standard non-myeloablative allogeneic HSCT on Day 0. Patients also receive oral mycophenolate mofetil daily beginning on Day 0 and continuing until Day 28. Participants receive an intravenous infusion of allogeneic cluster of differentiation 8 (CD8)+ memory T-cells over 10 to 20 minutes sometime between day 30 and day 60.

PRIMARY OBJECTIVES:

I. To determine the rate of conversion to full-donor chimerism (FDC) following a post-transplant infusion (Day 30-60) of freshly-enriched allogeneic CD8+ memory T-cells in patients with acute myeloid leukemia (AML), non-Hodgkin lymphoma (NHL), chronic lymphocytic leukemia (CLL), or Hodgkin lymphoma (HL), who received standard non-myeloablative total lymphoid irradiation (TLI) anti-thymocyte globulin (ATG) transplant conditioning.

SECONDARY OBJECTIVES:

I. To determine the risk of disease progression, overall and event free survival, and non-relapse mortality.

II. To determine the incidence of acute and chronic graft-versus-host disease (GVHD) following the infusion of allogeneic CD8+ memory T-cells.

OUTLINE:

Patients undergo TLI on days -11 to -7 and -4 to -1 and receive ATG per standard institutional practice on days -11 to -7. Patients also receive cyclosporine orally (PO) daily starting on day -3 and will continue for at least 6 months post-transplant. Patients undergo non-myeloablative allogeneic hematopoietic stem cell transplant (HSCT) on day 0. Patients also receive mycophenolate mofetil PO daily beginning on day 0 and continue until day 28. Based on the patient's status after the initial transplant, patients receive CD8+ memory T-cells intravenously (IV) over 10-20 minutes sometime between day 30 and day 60.

After completion of study treatment, patients are followed up periodically.

Eligibility Criteria:
Inclusion Criteria:

* Must have a human leukocyte antigen (HLA)-matched or single allele-mismatched adult sibling serving as donor
* Must have a myeloid or lymphoid malignant disease that is treated with TLI and ATG reduced intensity conditioning for allogeneic transplant (any of the following AML, myelodysplastic syndrome \[MDS\], myeloproliferative disease \[MPD\], CLL, B or T-cell NHL, HL)
* Patients who due to age, pre-existing medical conditions, or, prior therapy are considered to be at high risk for regimen related toxicity associated with fully ablative transplant conditioning, and therefore reduced intensity conditioning is recommended
* Ability to understand and the willingness to sign a written informed consent document; patients must have signed informed consent to participate in the trial
* DONOR: Must be an HLA-matched or single allele mismatched sibling of enrolled transplant patient
* DONOR: Must be 18-75 years of age, inclusive
* DONOR: Must be in a state of general good health and have completed a donor evaluation with history, medical examination and standard blood tests within 35 days of starting the hematopoietic cell collection procedure; in order to fairly represent the interests of the donor, the donor evaluation and consent will be performed by a study team member other than the recipient's attending physician
* DONOR: Must have a white blood cell count \> 3.5 x 10\^9/liter, platelets \> 150 x 10\^9/liter and hematocrit \> 35%
* DONOR: Must be capable of undergoing leukapheresis
* DONOR: Must be able to understand and sign informed consent
* DONOR: Must not be seropositive for HIV 1 and 2, hepatitis B surface antigen, hepatitis C antibody, human T-lymphotropic virus (HTLV) antibody, cytomegalovirus (CMV) immunoglobulin M (IgM), or rapid plasma reagin (RPR) (Treponema); donors with prior evidence of hepatitis B core antibody positivity will have a polymerase chain reaction (PCR) test done to evaluate for hepatitis B infection; donors with a positive hepatitis B PCR test are excluded
* DONOR: Females must not be pregnant or lactating
* DONOR: Must not have psychological traits or psychological or medical conditions which make them unlikely to tolerate the procedure
* DONOR: Must not have developed a new malignancy requiring chemotherapy or radiation in the interval since apheresis for initial hematocrit (HCT)
* PATIENT CRITERIA FOR PROCEEDING WITH CD8+ MEMORY T-CELL INFUSION:
* Patients must be beyond day 30 and before day 60 after transplant
* Patients must have evidence of mixed CD3 T-cell chimerism based on the day +28 (+/- 7 days) blood sample showing \>= 5% and =\< 95% donor type cells
* Patients must have no evidence of active graft-versus-host disease at the time of the CD8+ memory T-cell infusion; patients with a history of acute GVHD overall grade II based on skin only involvement or upper gastrointestinal (GI) tract involvement only will be eligible; patients with a history of liver or lower GI tract GVHD will not be eligible
* Patients must be on single immune suppression therapy with either tacrolimus or cyclosporine at the time of CD8+ memory T-cell infusion; prednisone at a physiologic dose of 5 mg per day or less is allowed
* Patients must have a Karnofsky performance status of \>= 60% at the time of the CD8+ memory T-cell infusion
* Patients must not have an uncontrolled bacterial, fungal or viral infection, defined as progressive symptoms despite therapy, at the time of the CD8+ memory T-cell infusion; asymptomatic viremia is allowed
* Patients must have adequate organ function and performance status at the time of the CD8+ memory T-cell infusion, defined by the following:

  * Total bilirubin =\< 4 mg/dL
  * SGOT or SGPT =\< 4 x ULN
  * Creatinine =\< 3 mg/dL or estimated creatinine clearance \>= 40ml/min

Exclusion Criteria:

* Uncontrolled bacterial, viral or fungal infection defined as currently taking medication and progression of clinical symptoms
* Progressive hemato-lymphoid malignancy despite conventional therapy
* Acute leukemia not in remission
* Chronic myelogenous leukemia (CML)
* Active central nervous system (CNS) involvement of the underlying malignancy
* Human immunodeficiency virus (HIV) positive
* Pregnant or lactating
* Prior malignancy (EXCEPTION: diagnosed \> 5 years ago without evidence of disease, OR treated =\< 5 years ago but have a greater than 50% chance of life expectancy of \>= 5 years for that malignancy)
* Have a psychiatric disorder(s) or psychosocial circumstance(s) which in the opinion of the primary physician would place the patient at an unacceptable risk from transplant
* Ejection fraction \< 30%, or uncontrolled cardiac failure
* Diffusing capacity of the lung for carbon monoxide (DLCO) \< 40% predicted
* Total bilirubin \> 3 mg/dL
* Serum glutamic oxaloacetic transaminase (SGOT) or serum glutamate pyruvate transaminase (SGPT) \> 4 x upper limit of normal (ULN)
* Creatinine \> 2 mg/dL and an estimated creatinine clearance =\< 40 mL/min
* Poorly controlled hypertension despite multiple antihypertensive medication OR
* Karnofsky performance status (KPS) \< 60%
* Note: Patients positive for hepatitis B and C will be evaluated on a case by case basis