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 with a diagnosis of CLL (or small lymphocytic lymphoma) or a diagnosis of CLL that progresses to prolymphocytic leukemia (PLL), or T-cell CLL or PLL * Hodgkin lymphoma (HL) - must have received and failed frontline therapy; patients must have failed or were not eligible for autologous transplant * Multiple myeloma (MM) - following a planned autologous transplant or equivalent high-dose therapy without a graft, or following a failed prior autograft * Acute myeloid leukemia (AML) - must have \< 5% marrow blasts at the time of transplant * Acute lymphoblastic leukemia (ALL) - must have \< 5% marrow blasts at the time of transplant * Chronic myelogenous leukemia (CML) - patients will be accepted beyond first chronic phase (CP1) if they have received previous myelosuppressive chemotherapy or HCT, and have \< 5% marrow blasts at time of transplant * Myelodysplastic syndromes/myeloproliferative disorders (MDS/MPD) - must have received previous myelosuppressive chemotherapy or HCT, and have \< 5% marrow blasts at time of transplant * Waldenstrom's macroglobulinemia - must have failed 2 courses of therapy * Myelosuppressive chemotherapy must be discontinued three weeks prior to conditioning with the exception of hydroxyurea or imatinib * Patients \< 12 years old must be approved by both the participating institutions' patient review committee such as the Patient Care Conference (PCC) at the Fred Hutchinson Cancer Research Center (FHCRC) and the FHCRC principal investigator * Patient who refused to be treated on a conventional HCT protocol; for this inclusion criterion, transplants must be approved by both the participating institution's patient review committee such as the Patient Care Conference (PCC) at the FHCRC and the FHCRC principal investigators * Patients with human leukocyte antigen (HLA)-matched related donors * Patients with renal failure are eligible; however, patients with renal compromise (serum creatinine \> 2.0) will likely have further compromise in renal function and may require hemodialysis (which may be permanent) due to the need to maintain adequate serum tacrolimus levels * DONOR: Related donor who is HLA genotypically identical at least at one haplotype and may be phenotypically or genotypically identical at the allele level at HLA-A, -B, -C, -DRB1, and -DQB1 * DONOR: Donor must consent to filgrastim (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: * Eligible for a high priority curative autologous transplant * Patient with rapidly progressive, aggressive NHL unless in minimal disease state * Patients with chronic myelomonocytic leukemia (CMML) * Life expectancy severely limited by diseases other than malignancy * Any current central nervous system (CNS) involvement with disease refractory to intrathecal chemotherapy * Presence of circulating leukemic blasts (in the peripheral blood) detected by standard pathology for patients with AML, ALL or CML * Fertile men or women unwilling to use contraceptives during and for up to 12 months post treatment * Female patients who are pregnant or breastfeeding * Human immunodeficiency virus (HIV)-positive patients * Patients with active non-hematologic malignancies (except non-melanoma skin cancers); this exclusion does not apply to patients with non-hematologic malignancies that do not require therapy * 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; this exclusion does not apply to patients with non-hematologic malignancies that do not require therapy * Fungal pneumonia with radiological progression after receipt of amphotericin formulation or mold-active azoles for greater than 1 month * Karnofsky score \< 50 for adult patients * Lansky-Play performance score \< 50 for pediatric patients * Symptomatic coronary artery disease or ejection fraction \< 35% or other cardiac failure requiring therapy (or, if unable to obtain ejection fraction, shortening fraction of \< 26%); ejection fraction is required if age \> 50 years or there is a history of anthracycline exposure or history of cardiac disease; patients with a shortening fraction \< 26% may be enrolled if approved by a cardiologist * Poorly controlled hypertension * Diffusing capacity of the lung for carbon monoxide (DLCO) \< 30%, total lung capacity (TLC) \< 30%, forced expiratory volume in one second (FEV1) \< 30% and/or receiving supplementary continuous oxygen; the FHCRC principal investigator (PI) of the study must approve enrollment of all patients with pulmonary nodules * 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, 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 or bridging fibrosis, 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 \> 3 mg/dL, and symptomatic biliary disease * Patients with active bacterial or fungal infections unresponsive to medical therapy * DONOR: Age less than 12 years * DONOR: Identical twin * DONOR: Pregnancy * DONOR: Infection with HIV * DONOR: Known allergy to filgrastim (G-CSF) * DONOR: Current serious systemic illness that would result in increased risk for G-CSF mobilization and harvest of peripheral blood stem cells (PBSC)