Targeted Marrow Irradiation, Fludarabine Phosphate, and Busulfan Before Donor Progenitor Cell Transplant in Treating Patients With Hematologic Malignancies

Inclusion Criteria: * Patients ineligible to receive full myeloablative conditioning regimen for allogeneic hematopoietic progenitor cell transplant due to age or comorbidities * Patients must have histologically or cytologically diagnosis of hematologic malignancies with an indication for allogeneic hematopoietic progenitor cell transplantation, who are ineligible to receive a full ablative conditioning regimen as part of their transplantation, including: * Acute myeloid leukemia * Acute lymphocytic leukemia * Non Hodgkin lymphoma * Hodgkin lymphoma * Multiple myeloma * Myelodysplastic syndrome * Chronic lymphocytic leukemia * Chronic myeloid leukemia: * Myeloproliferative syndromes including myelofibrosis * Complete remission is not necessary for enrollment in this protocol * Patients must have an allogeneic hematopoietic progenitor cell donor (HPCT), either a matched sibling, mismatched (1 allele) sibling, or a matched unrelated donor (MUD) or a mismatched (1 allele) unrelated donor * Previous hematopoietic progenitor cell transplantation is allowed; a minimum of 6 months should have elapsed from prior autologous hematopoietic progenitor cell transplantation and a minimum of 6 months should have elapsed since prior allogeneic hematopoietic progenitor cell transplantation; prior transplantation with conditioning regimens using total body irradiation is not allowed * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * Life expectancy of \> 12 weeks, in the opinion of and as documented by the investigator * Patients must have adequate hepatic, and renal function as defined below: there is no exclusion for the presence of cytopenias * Total bilirubin ≤ 1.5 times the institutional upper limit of normal * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) ≤ 2.5 X institutional upper limit of normal * Alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) ≤ 2.5 X institutional upper limit of normal * Creatinine clearance (calculated by the Cockroft-Gault formula) ≥ 60 ml/min * Pulmonary Function Tests (FEV1, FVC, DLCO) 40%. * Women of child-bearing potential and men must agree to use adequate contraception (double barrier method of birth control or abstinence) from the time of study entry, for the duration of study participation and for 3 months after completing treatment; should a woman become pregnant or suspect that she is pregnant while she or her partner is participating in this study, she should inform the treating physician immediately * Subjects must have the ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Prior non-hematologic treatment toxicities must be resolved to ≤ grade 1 according to National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) version 4.0, with the exception of the following grade 2 toxicities: alopecia; dry skin; spleen disorders, hearing impairment; tinnitus; hypothyroidism; hyperthyroidism; endocrine disorders; blurred vision; cataracts; constipation; gastroesophageal reflux; fatigue; abnormal coagulation tests INR and/or aPTT; weight gain or weight loss; anorexia; glucose intolerance; hypoalbuminemia; hypokalemia; muscle weakness; dysgeusia; paresthesias; peripheral motor and/or sensory neuropathy; hot flashes; hypertension. * Patients must not have received other investigational agents within 14 days of initiation of the conditioning regimen * Patients with untreated brain metastases should be excluded from this clinical trial * History of allergic reactions attributed to compounds of similar chemical or biologic composition to fludarabine and or busulfan or other agents used in this study * Prior allogeneic hematopoietic progenitor cell transplantation * Prior autologous hematopoietic progenitor cell transplantation if the conditioning regimen included total body irradiation * Patients with uncontrolled intercurrent illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements; this exclusion criterion does not include the underlying disease for which the patient is undergoing hematopoietic progenitor cell transplantation * Pregnant or breastfeeding women are excluded from this study; breastfeeding should be discontinued * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible * Patients with a history of therapy with radiation therapy are excluded * Due to technical limitations of TMI, patients must be no taller than 1.9 m (6 feet 4 inches), and no wider from elbow to elbow in the supine position than 60 cm.