Fludarabine Phosphate and Total-Body Radiation Followed by Donor Peripheral Blood Stem Cell Transplant and Immunosuppression in Treating Patients With Hematologic Malignancies

Inclusion Criteria: * Patients with non-Hodgkin lymphoma (NHL), chronic lymphocytic leukemia (CLL) or multiple myeloma who are not eligible for a curative autologous transplantation or who have received a prior autologous transplantation; patients with NHL or CLL must have failed prior therapy with an alkylating agent and/or fludarabine, or be at high risk of relapse; patients with multiple myeloma must have stage II or III disease and received prior chemotherapy * Patients \< 50 years of age with NHL, Hodgkin's disease (HD), CLL or multiple myeloma at high risk of regimen related toxicity through prior autologous transplant or through pre-existing medical conditions * Patients \< 75 years of age with other malignant diseases treatable by allogeneic bone marrow transplant (BMT) whom through pre-existing chronic disease affecting kidneys, liver, lungs, and heart are considered to be at high risk for regimen related toxicity using standard high dose regimens; the following diseases are the likely candidates * Myelodysplastic syndromes * Myeloproliferative syndromes * Acute Leukemia with \< 10% blasts * Amyloidosis * Hodgkin's disease * The Fred Hutchinson Cancer Research Center (FHCRC) Patient Care Conference (PCC) may approve patients with other malignancies or patients declining standard allografts for transplant following presentation and approval; centers outside the FHCRC that have a PCC or equivalent should obtain their Institutional approval; if there is not a comparable group at the Institution, please contact the FHCRC Principal Investigator for FHCRC approval through PCC * DONOR: Human leukocyte antigen (HLA) genotypically or phenotypically identical related donor * 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 * Patients with rapidly progressive aggressive NHL unless in minimal disease state * Any current central nervous system (CNS) involvement with disease * Fertile men or women unwilling to use contraceptive techniques during and for 12 months following treatment * Females who are pregnant * Patients who are human immunodeficiency virus (HIV) positive * Cardiac ejection fraction \< 40%; ejection fraction is required if the patient has a history of anthracyclines or history of cardiac disease * Receiving supplementary continuous oxygen * Diffusing capacity of the lung for carbon monoxide (DLCO) \< 30% * Total lung capacity (TLC) \< 30% * Forced expiratory volume in one second (FEV1) \< 30% * Total bilirubin \> 2x the upper limit of normal * Serum glutamate pyruvate transaminase (SGPT) and serum glutamic oxaloacetic transaminase (SGOT) 4x the upper limit of normal * Karnofsky score \< 50 * Patients with poorly controlled hypertension who are unable to have blood pressure kept below 150/90 on standard medication * Patients with renal failure are eligible, however patients with renal compromise (serum creatinine greater than 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 cyclosporine levels * The addition of cytotoxic agents for "cytoreduction" with the exception of hydroxyurea and imatinib mesylate will not be allowed within two weeks of the initiation of conditioning * DONOR: Identical twin * DONOR: Age less than 12 years * DONOR: Pregnancy * DONOR: Infection with HIV * DONOR: Inability to achieve adequate venous access * DONOR: Known allergy to G-CSF * DONOR: Current serious systemic illness