Reduced Intensity Chemotherapy and Radiation Therapy Before Donor Stem Cell Transplant in Treating Patients With Hematologic Malignancies

Patients treated on this study will have:

* Acute myeloid leukemia in morphologic complete remission (CR) not requiring treatment for their disease for 4 weeks

* A history of acute myeloid leukemia (AML) with \< 10% residual blasts (use highest count on staging studies) after induction therapy and persisting with \< 10% blasts for at least 8 weeks without reinduction and at the time of HSCT

* Refractory anemia (RA) or refractory anemia with ring sideroblasts (RARS) or isolated 5q-

* Refractory anemia with excess blasts (RAEB)-1, refractory cytopenia with multilineage dysplasia (RCMD)+/-ringed sideroblasts (RS), or myelodysplastic syndrome (MDS) not otherwise specified (NOS) with stable disease for at least 3 months

* RAEB-2 must demonstrate chemo-responsiveness; chemo-responsiveness is defined as a persistent blast percentage decrease by at least 5 percentage points to therapy and there must be =\< 10% blasts (use highest count on staging studies) after treatment and at the time of transplant

* Hodgkin or Indolent non-Hodgkin's lymphoma

* Myeloma with \< 5% plasma cells in the marrow

* Myeloproliferative disorders (excludes chronic myelomonocytic leukemia \[CMML\])

* Aplastic anemia

* A hematological or oncological disease (not listed) in which allogeneic HSCT is thought to be beneficial, and the disease is chemoresponsive

* Patients without clear manifestation of their disease status in terms of stage and/or responsiveness should be discussed with the principal investigator (PI) and enrollment analysis should be documented in the study records

Patients must have a related donor who is human leukocyte antigen (HLA) mismatched at 2, 3, or 4 antigens at the HLA-A; B; C; DR loci in the graft-versus-host disease (GVHD) direction; (patients with related donors who are HLA identical or are a 1-antigen mismatch may be treated on this therapeutic approach, but will have their outcomes will not be part of the statistical aims of the study); the HLA matched related category includes patients with a syngeneic donor

Patients must have had front line therapy for their disease

LVEF (left ventricular end diastolic function) of \>= 45%

DLCO (diffusing capacity of the lung for carbon monoxide) \>= 45% of predicted corrected for hemoglobin, FEV-1 (forced expiratory volume at 1 second) \>= 50% of predicted

Serum bilirubin =\< 1.8

Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) =\< 2.5 X upper limit of normal

Creatinine clearance of \>= 60 mL/min

HCT-CI/age score =\< 5 points (patients with greater than 5 points will be allowed for trial with approval of the PI and the co-PI or his designee; this is an adjustment to account for healthy patients who meet the spirit of this protocol but have histories that result in higher than HCT-CI 5 points; an example is a patient with a solid tumor malignancy in their remote history \[adds 3 points to HCT-CI total\] where the treatment for the malignancy occurred years to decades before and there has been complete recovery of toxicities)

Karnofsky performance status (KPS) \>= 90% patients older than 70 years, KPS \>= 80% patients younger than 70 years

Patients must be willing to use contraception if they have childbearing potential

What this study is about