Azacitidine After Chemotherapy and Donor Lymphocyte Infusion in Patients With Relapsed Acute Myeloid Leukemia or Myelodysplastic Syndrome Previously Treated With Donor Stem Cell Transplant

PATIENT Inclusion Criteria: * Must have a diagnosis of AML/MDS based on 2008 World Health Organization (WHO) classification of myeloid malignancies * Must have laboratory, histologic, or cytogenetic evidence of disease relapse after allogeneic hematopoietic stem cell transplant (HSCT) and require salvage therapy followed by DLI * Must have original donor * Must have life expectancy \>= 2 months * Must be ≥ 18 years old. Azacitidine is not approved by the FDA for use in children * Must have an Eastern Cooperative Oncology Group (ECOG) performance status =\< 3 * Must have laboratory results indicating: * Total bilirubin \< 2.0 mg/dL * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 3 X the upper limit of institutional normal * Serum creatinine =\< 2.0 mg/dL * Patient must have ability to understand and willingness to provide written informed consent prior to participation in the study and any related procedures being performed * The effects of 5-AzaC on the developing human fetus at the recommended therapeutic dose are unknown; for this reason and because category D agents as well as other therapeutic agents used in this trial are known to be teratogenic, women of childbearing age must have a negative serum pregnancy test (Beta \[B\]-human chorionic gonadotropin) within 72 hours prior to initiating therapy and be willing to not become pregnant by using effective contraception while undergoing treatment and for at least 3 months afterwards; azacitidine is a pregnancy category D drug and could be harmful to or cause loss of a fetus; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Men must be willing not to father a new child while receiving therapy; they must use an effective barrier method of contraception during the study and for 3 months following the last dose * Both men and women and members of all races and ethnic groups are eligible for this trial DONOR Inclusion Criteria: * Must be the original donor for the allogeneic bone marrow transplant patient * Must have signed the standard informed consent form; if sufficient cryopreserved cells remain from a previous donation, no additional donation or consent is required * Must be eligible according to Washington University "Guidelines for Eligibility of Normal Donors" or per National Marrow Donor Program (NMDP) standards if unrelated donor * Both men and women and members of all races and ethnic groups are eligible for this trial PATIENT Exclusion Criteria: * Must not have Grade III-IV GVHD * Must not have an advanced malignant hepatic tumor * Must not receive anti-thymocyte globulin, campath (alemtuzumab) or daclizumab within 4 weeks of DLI * Must not receive any other forms of chemotherapy after cell infusion during the treatment protocol * Must not be receiving any other investigational agents within 14 days of first dose of study drug * Must not have uncontrolled intercurrent illness including ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, or psychiatric illness/social situations that would limit compliance with study requirements * Must not be pregnant or breastfeeding; pregnant women are excluded from this study because azacitidine is a Category D agent with the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with azacitidine, breastfeeding should be discontinued if the mother is treated with azacitidine; these potential risks may also apply to other agents used in this study * Must not have a history of allergic reactions attributed to compounds of similar chemical or biologic composition to azacitidine or other agents used in the study * Must not have a known or suspected hypersensitivity to azacitidine or mannitol. * Must not be human immunodeficiency virus (HIV)-positive and on combination antiretroviral therapy; these patients are ineligible because of the potential for pharmacokinetic interactions with azacitidine; in addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy; appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated DONOR Exclusion Criteria: * Must not have any underlying conditions which would contra-indicate apheresis * Must not be pregnant