Total-Body Irradiation With or Without Fludarabine Phosphate Followed By Donor Stem Cell Transplant in Treating Patients With Hematologic Cancer

Inclusion Criteria: * Patients 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 * An autograft immediately prior (less than 6 months) to nonmyeloablative HCT (tandem approach) is not permitted * Patients with hematologic malignancies treatable with HCT or with a B cell malignancy except those curable with autologous transplant will be included * Aggressive non-Hodgkin lymphomas (NHLs) and other histologies such as diffuse large B cell NHL: patients are eligible IF they are not eligible for autologous hematopoietic stem cell transplantation (HSCT), not eligible for conventional myeloablative HSCT, or have failed an autologous HSCT * Low grade NHL with \< 6 month duration of complete remission (CR) between courses of conventional therapy * Mantle cell NHL; may be treated in first CR * Chronic lymphocytic leukemia (CLL) must have either: * 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. cladribine \[2-CDA\], pentostatin) or experience disease relapse within 12 months after completing therapy with a regimen containing FLU (or another nucleoside analog) * Failed FLU-cyclophosphamide \[CY\]-rituximab (FCR) combination chemotherapy at any time point * Have "17p deletion" cytogenetic abnormality; patients should have received induction chemotherapy but could be transplanted in 1st CR * Or patients with a diagnosis of CLL (or small lymphocytic lymphoma) or 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): must have chemosensitive disease after failed autografting (an autografting immediately prior \[within 6 months\] to nonmyeloablative HCT \[tandem approach\] is not permitted) * Acute myeloid leukemia (AML): must have \< 5% marrow blasts at the time of transplant and be beyond first CR * Acute lymphocytic leukemia (ALL): must have \< 5% marrow blasts at the time of transplant and be beyond first CR * Chronic myelogenous leukemia (CML): patients will be accepted in chronic phase (CP) beyond CP1 if they have received previous myelosuppressive chemotherapy or HCT, \< 5% marrow blasts at time of transplant * Myelodysplastic syndromes (MDS)/myeloproliferative disorders (MPD): must have received previous myelosuppressive chemotherapy or HCT, \< 5% marrow blasts at time of transplant * Waldenstroms Macroglobulinemia: must have failed 2 courses of therapy * Patients will not be allowed to receive myelosuppressive chemotherapy for three weeks prior to conditioning * 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 * Patients 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 investigator * Patients with human leukocyte antigen (HLA)-matched related donors * 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) * DONOR: For females of child bearing age, serum pregnancy qualitative (PGSTAT) within 72 hours prior to initial dose of filgrastim (G-CSF); results must be available prior to filgrastim Exclusion Criteria: * Eligible for a high priority curative autologous transplant * Patients with rapidly progressive, aggressive NHL unless in minimal disease state * Patients with chronic myelomonocytic leukemia * Presence of circulating leukemic blasts (in the peripheral blood) detected by standard pathology for patients with AML, ALL or CML * Life expectancy severely limited by diseases other than malignancy * Any current central nervous system (CNS) involvement with disease refractory to intrathecal chemotherapy * 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-hematological malignancies (except localized non-melanoma skin malignancies) * 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 * Fungal infections with radiological progression after receipt of amphotericin formulation or mold-active azoles for greater than 1 month * Patients with active bacterial or fungal infections unresponsive to medical therapy * Karnofsky score \< 50 for adult patients * Lansky-Play performance score \< 50 for pediatric patients * The addition of cytotoxic agents for "cytoreduction" with the exception of tyrosine kinase inhibitors (imatinib mesylate), cytokine therapy, hydroxyurea, low dose cytarabine, chlorambucil, or rituxan will not be allowed within three weeks of the initiation of conditioning * Patients with the following organ dysfunction: * Symptomatic coronary artery disease or ejection fraction \< 35% or other cardiac failure requiring therapy (required for patients with history of cardiac disease or anthracycline use); ejection fraction is required if age \> 50 years or there is a history of anthracycline exposure or history of cardiac disease * Poorly controlled hypertension on multiple antihypertensives * Pulmonary: diffusion capacity of 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 study principal investigator (PI) 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, 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 \> 3 mg/dL, and symptomatic biliary disease * DONOR: Age less than 12 years * DONOR: Identical twin * DONOR: Pregnancy * DONOR: Infection with HIV * DONOR: Known allergy to filgrastim * DONOR: Current serious systemic illness that would result in increased risk for filgrastim mobilization and harvest of PBSC