Tacrolimus and Mycophenolate Mofetil in Preventing Graft-Versus-Host Disease in Patients Who Have Undergone Total-Body Irradiation With or Without Fludarabine Phosphate Followed by Donor Peripheral Blood Stem Cell Transplant for Hematologic Cancer

Inclusion Criteria: * Patient must be not eligible for conventional allogeneic hematopoietic cell transplantation (HCT) and must have disease expected to be stable for at least 100 days without chemotherapy; patients with hematologic malignancies treatable with HCT or with a B cell malignancy except those curable with autologous transplant will be included; patients not eligible for active disease specific protocols may be enrolled in this protocol; patients will include the following * Diffuse large B cell non-Hodgkin lymphoma (NHL) and other aggressive lymphomas - not eligible for conventional myeloablative HCT or after autologous HCT * Low grade NHL- with \< 6 months duration of complete response (CR) between courses of conventional therapy * Mantle cell NHL- may be treated in first CR * Chronic lymphocytic leukemia (CLL) - must have either 1) failed to meet National Cancer Institute (NCI) Working Group criteria for complete or partial response after therapy with a regimen containing fludarabine phosphate (FLU) (or another nucleoside analog, e.g. 2-chlorodeoxyadenosine \[2-CDA\], pentostatin) or experience disease relapse within 12 months after completing therapy with a regimen containing FLU (or another nucleoside analog); 2) failed FLU-cyclophosphamide (CY)-Rituximab (FCR) combination chemotherapy at any time point; or 3) have "17p deletion" cytogenetic abnormality; patients should have received induction chemotherapy but could be transplanted in 1st CR; 4) patients wit…