This clinical trial studies how well giving fludarabine phosphate together with total-body irradiation (TBI) before donor peripheral blood stem cell transplant works in treating patients with chronic lymphocytic leukemia or small lymphocytic leukemia. Giving low doses of chemotherapy, such as fludarabine phosphate, and TBI before a donor peripheral blood stem cell transplant helps stop the growth of cancer cells. Giving chemotherapy before or after peripheral blood stem cell transplant also stops 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-tumor effect). Sometimes the transplanted cells from a donor can also make an immune response against the body's normal cells. Giving cyclosporine and mycophenolate mofetil before and after the transplant may stop this from happening.

PRIMARY OBJECTIVES:

I. To determine whether nonmyeloablative allogeneic hematopoietic stem cell transplantation (HSCT) from matched-related donors can improve the probability of survival 18 months after treatment for fludarabine (fludarabine phosphate)-refractory, fludarabine phosphate, cyclophosphamide, and rituximab (FCR)-failed, or del 17p chronic lymphocytic leukemia (CLL) beyond that observed in historical controls (30%).

SECONDARY OBJECTIVES:

I. To assess the rate of relapse with allogeneic HSCT using nonmyeloablative conditioning for patients with fludarabine-refractory, FCR-failed, or del 17p CLL compared with historical data on autologous HSCT.

II. To estimate the incidence of grade 2-4 acute graft-versus-host disease (GVHD) and chronic GVHD in patients with CLL treated with low-dose TBI, fludarabine, peripheral blood stem cell (PBSC) infusion and immunosuppression with cyclosporine and mycophenolate mofetil.

III. To characterize the rate and types of infections with this regimen.

IV. To estimate the rate of transplant-related mortality in the first 200 days.

OUTLINE:

NONMYELOABLATIVE CONDITIONING: Patients receive fludarabine phosphate intravenously (IV) on days -4 to -2 and TBI on day 0.

TRANSPLANT: Patients undergo allogeneic peripheral blood stem cell transplant on day 0.

GVHD PROPHYLAXIS: Patients receive cyclosporine orally (PO) every 12 hours on days -3 to 180 with taper beginning on day 56 and mycophenolate mofetil PO every 12 hours on days 0-27.

After completion of study treatment, patients are followed up at 12 and 18 months and then annually for 5 years.

Inclusion Criteria:

• Patients with CLL (or small lymphocytic lymphoma) or diagnosis of CLL that progresses to prolymphocytic leukemia (PLL), or T-cell CLL or PLL
• Patients with B-Cell CLL or PLL who have at least one of the following:
• Failed to meet National Cancer Institute (NCI) Working Group criteria for complete or partial response after therapy with a regimen containing fludarabine (or another nucleoside analog, e.g. cladribine [2-CDA], pentostatin) or experience disease relapse within 12 months after completing therapy with a regimen containing fludarabine (or another nucleoside analog)
• Failed FCR combination chemotherapy at any time point
• Had de novo of acquired "17p deletion" cytogenetic abnormality; patients should have received induction chemotherapy but could be transplanted in first (1st) complete response (CR)
• Patient has a suitable human leukocyte antigen (HLA)-matched related donor who is willing to undergo leukapheresis initially for collection of PBSC and subsequently for collection of peripheral blood mononuclear cells (PBMC) with filgrastim (G-CSF) mobilization and willing to donate stem cells
• DONOR: Related donor who is HLA phenotypically or genotypically identical at the allele level at HLA-A, -B, -C, -DRB1, and -DQB1
• DONOR: Donor must consent to G-CSF administration and leukapheresis
• DONOR: Donor must have adequate veins for leukapheresis or agree to placement of central venous catheter (femoral, subclavian)

Exclusion Criteria:

• Infection with human immunodeficiency virus (HIV), human T-lymphotropic virus (HTLV)-1, or HTLV-2
• Active central nervous system (CNS) involvement with CLL
• Patients with active non-hematologic malignancies (except non-melanoma skin cancers)
• Patients with a history of non-hematologic malignancies (except non-melanoma skin cancers) currently in a complete remission, who are less than 5 years from the time of complete remission, and have a > 20% risk of disease recurrence
• Fertile men or women unwilling to use contraceptive techniques during and for 12 months following treatment
• Pregnant or breastfeeding women
• Karnofsky score =< 70
• Fungal infections with radiological progression after receipt of amphotericin B or active triazole for greater than 1 month
• Cytotoxic agents for "cytoreduction" (with the exception of imatinib mesylate [Gleevec], cytokine therapy, hydroxyurea, chlorambucil or Rituxan) within three weeks of the initiation of conditioning
• Active bacterial or fungal infections unresponsive to medical therapy
• Cardiovascular: cardiac ejection fraction < 40%; patients with poorly controlled hypertension despite multiple antihypertensives
• Pulmonary: diffusing capacity of carbon monoxide (DLCO) < 40%, total lung capacity (TLC) < 40%, forced expiratory volume in one second (FEV1) < 40% and/or requiring continuous supplementary oxygen, or severe deficits in pulmonary function testing as defined by pulmonary consultant service
• Liver function abnormalities: patients with clinical or laboratory evidence of liver disease would be evaluated for the cause of liver disease, its clinical severity in terms of liver function, bridging fibrosis, and the degree of portal hypertension; patients will be excluded if they are found to have fulminant liver failure, cirrhosis of the liver with evidence of portal hypertension, alcoholic hepatitis, esophageal varices, a history of bleeding esophageal varices, hepatic encephalopathy, uncorrectable hepatic synthetic dysfunction evinced by prolongation of the prothrombin time, ascites related to portal hypertension, bacterial or fungal liver abscess, biliary obstruction, chronic viral hepatitis with total serum bilirubin > 3mg/dL, or symptomatic biliary disease
• DONOR: Age < 12 years
• DONOR: Identical twin
• DONOR: Pregnancy
• DONOR: Infection with HIV
• DONOR: Inability to achieve adequate venous access
• DONOR: Known allergy to filgrastim (G-CSF)
• DONOR: Current serious systemic illness