Fludarabine Phosphate, Low-Dose Total-Body Irradiation, and Donor Stem Cell Transplant Followed by Cyclosporine, Mycophenolate Mofetil, Donor Lymphocyte Infusion in Treating Patients With Hematopoietic Cancer

Inclusion Criteria: * Patients aged \> 49 years and \< 75 years with non-Hodgkin lymphoma (NHL), chronic lymphocytic leukemia (CLL) and multiple myeloma who are not eligible for a curative autologous transplantation or who have failed prior autologous transplantation; patients with NHL and 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, 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 * Renal cell carcinoma * Patients with other malignancies declining standard allografts may be approved for transplant following presentation and approval by the Fred Hutchinson Cancer Research Center (FHCRC) chimerism group * DONOR: * Human leukocyte antigen (HLA) genotypically or phenotypically identical related donor * Donor must consent to granulocyte colony-stimulating factor (G-CSF) administration and leukopheresis * Donor must have adequate veins for leukopheresis or agree to placement of central venous catheter (femoral, subclavian) * Age \< 75 years Exclusion Criteria: * Eligible for a high-priority curative autologous transplant * Patients with rapidly progressive aggressive NHL unless in minimal disease state * Active 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% * Severe defects in pulmonary function testing (defects are currently categorized as mild, moderate and severe) as defined by the pulmonary consultant, or receiving supplementary continuous oxygen * Total bilirubin \> 2 x the upper limit of normal * Serum glutamate pyruvate transaminase (SGPT) and serum glutamic oxaloacetic transaminase (SGOT) 4 x the upper limit of normal * Karnofsky score \< 50 * Patients with poorly controlled hypertension * 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 * DONOR: * Identical twin * Age less than 12 years * Pregnancy * Infection with HIV * Inability to achieve adequate venous access * Known allergy to G-CSF * Current serious systemic illness