Guadecitabine and Donor Lymphocyte Infusion in Treating Patients With Acute Myeloid Leukemia or Myelodysplastic Syndrome Relapsing After Allogeneic Stem Cell Transplant

Inclusion Criteria: * Diagnosis of acute myeloid leukemia (AML) and myelodysplastic syndrome (including chronic myelomonocytic leukemia \[CMML\]) according to WHO classification that underwent first allogeneic hematopoietic cell transplant (HSCT) with either peripheral blood or bone marrow as the source of the hematopoietic stem cells * No more than 1 antigen mismatch at human leukocyte antigen (HLA)-A, B, C, DRB1 and DQB1 locus for either related or unrelated donor * High risk AML and MDS patients will be included * Cohort 1: morphological relapse after stem cell transplant: * MDS patients: re-appearance of dysplastic changes in the bone marrow, with or without increase in bone marrow last count, which is pathologically consistent with myelodysplastic syndrome; * AML patients: bone marrow blast count \>= 5% * Cohort 2: Persistence or reappearance of minimal residual disease by flow cytometry or cytogenetic or molecular testing while being in morphological remission after allogeneic stem cell transplantation * Cohort 3: High risk AML and MDS patients who are in complete remission morphologically with no evidence of minimal residual disease by flow cytometry or cytogenetic or molecular testing after allogeneic stem cell transplantation * MDS patients: * Cytogenetics consistent with poor or very poor risk group by 5-risk classification; * Cytogenetics consistent with monosomal karyotype * Bone marrow blast count \> 5% but less than 20% at any time during their disease course before HSCT * Peripheral blood blast =\< 5% at HSCT * Therapy-related MDS * AML patients: * Cytogenetics and molecular features consistent with adverse risk group by European LeukemiaNet classification for AML; * Presence of minimal residual disease by multi-color flow cytometry or cytogenetics or molecular studies at the time of HSCT; * Presence of active disease defined as bone marrow blast count \> 5% but less than =\< 10% at the time of HSCT * Peripheral blood blast count =\< 5% at HSCT * Therapy-related AML * Be able to start the drug therapy between 42 to 100 days following allogeneic SCT; * No more than 1 prior allogeneic SCT * Post-transplant bone marrow consistent with complete remission with no evidence of minimal residual disease by flow-cytometry or cytogenetics or molecular testing * Adequate engraftment within 14 days prior to starting study drug: absolute neutrophil count (ANC) \>= 1.0 x 10\^9/L without daily use of myeloid growth factor; and, platelet \>= 50 x 10\^9/L without platelet transfusion within 1 week * Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2 * Serum creatinine =\< 1.5 mg/dL or creatinine clearance greater or equal than 40 cc/min as defined by the Cockcroft-Gault equation * Serum bilirubin =\< 1.5 x upper limit of normal (ULN) * Aspartate transaminase (aspartate aminotransferase \[AST\]) or alanine transaminase (alanine aminotransferase \[ALT\]) =\< 2.5 x ULN * Alkaline phosphatase =\< 2.5 x upper limit (UL) * No active bleeding * No uncontrolled graft versus host disease (GVHD) * No clinical evidence of life-threatening infection * Capable of understanding the investigational nature, potential risks and benefits of the study, and able to provide valid informed consent * Human immunodeficiency virus (HIV) negative and hepatitis B surface antigen (HBs-Ag) negative * Negative serum or urine pregnancy test for women with reproductive potential; the only subjects who will be exempt from this criterion are postmenopausal women (defined as women who have been amenorrheic for \> 12 months) or subjects who have been surgically sterilized or otherwise proven sterile Exclusion Criteria: * Use of any anti-leukemic agents after relapse is documented (note that the use of these anti-leukemic agents given as post-transplant maintenance therapy is allowed in this study, e.g., subcutaneous or oral 5-azacytidine or FLT3 inhibitors for maintenance) for cohorts 1 and 2 * Bone marrow blast count \> 60% for cohort 1 * Use of any of the following after transplantation and prior to starting study therapy for cohort 3: * Investigational agents/therapies * Anti-leukemic agents given as post-transplant maintenance therapy (e.g., subcutaneous or oral 5-azacytidine or FLT3 inhibitors for maintenance) * Active acute graft versus host disease (GVHD) grade II or higher * Active chronic GVHD that is extensive * Concurrent use of systemic immune suppressive other than calcineurin inhibitors and sirolimus * Active uncontrolled systemic fungal, bacterial or viral infection * Symptomatic or uncontrolled arrhythmias * Significant active cardiac disease within the previous 6 months, including: New York Heart Association (NYHA) class III or IV congestive heart failure; unstable angina or angina requiring surgical or medical intervention, and/or; myocardial infarction * Known active viral infection with human immunodeficiency virus (HIV), hepatitis B virus (HBV) or hepatitis C virus (HCV) * Prior history of solid tumor unless the subject has been free of the disease for \>= 1 year; however, subjects with the following history/concurrent conditions are allowed: basal or squamous cell carcinoma of the skin; carcinoma in situ of the cervix; carcinoma in situ of the breast; incidental histologic finding of prostate cancer (T1a or T1b using the tumor, node, metastasis \[TNM\] clinical staging system)