Fludarabine Phosphate, Low-Dose Total Body Irradiation, and Donor Stem Cell Transplant in Treating Patients With Hematologic Malignancies or Kidney Cancer

Inclusion Criteria: * Age \> 50 years with hematologic malignancies treatable by allogeneic hematopoietic stem cell transplant (HSCT) and all patients with B cell malignancies except those who may be cured by autologous stem cell transplantation (SCT) * Age =\< 50 years of age with hematologic diseases treatable by allogeneic HSCT who through pre-existing medical conditions or prior therapy are considered to be of high risk for regimen related toxicity associated with a conventional transplant or those patients who refuse a conventional SCT; transplants must be approved for these inclusion criteria by both the participating institution's patient review committee such as the Patient Care Conference (PCC at the Fred Hutchinson Cancer Research Center \[FHCRC\]) and by the principal investigator * Patients with metastatic renal cell carcinoma with the histologic subtypes of clear cell, papillary and medullary may be accepted regardless of age * The following diseases will be permitted although other diagnoses can be considered if approved by PCC or the participating institution's patient review committees and the principal investigator * Non-Hodgkin lymphoma (NHL), chronic lymphocytic leukemia (CLL), Hodgkin lymphoma (HL) - must have received and failed frontline therapy * Multiple myeloma - must have received prior chemotherapy; consolidation of chemotherapy by autografting prior to nonmyeloablative HSCT is permitted * Acute myeloid leukemia (AML)/acute lymphoblastic leu…