5-Fluoro-2'-Deoxycytidine and Tetrahydrouridine in Treating Patients With Acute Myeloid Leukemia or Myelodysplastic Syndromes

Inclusion Criteria: Patients must have the following diagnosis: * Acute myeloid leukemia * Relapsed or refractory * Newly diagnosed in patients age 60 and above or of any age unable to receive standard induction regimen * Patients with MDS with an International Prognostic Scoring System (IPSS) score \>= 0.5 * Newly diagnosed * Relapsed or refractory * Any prior therapy must have been completed \>= 2 weeks prior to enrollment and the participant must have recovered to eligibility levels from prior toxicity * No limit to number of prior regimens * Hydroxyurea is allowed prior to enrollment to keep white blood cell count (WBC) below 20 K * Valproic acid not being used for seizure control should be stopped 72 hours before starting therapy * Prior therapy with hypomethylating agent (decitabine or azacitidine) is allowed and must be completed \>= 6 weeks prior to enrollment * Relapsed patients are eligible post allogeneic or matched unrelated donor (MUD) transplant after 100 days; there should be no active acute graft versus host disease of any grade and patient should not be receiving immunosuppression for acute graft versus host disease; the patient must not have Chronic Graft versus Host disease (cGvHD) other than mild skin, oral, or ocular cGvHD not requiring systemic immunosuppression * Relapsed patients are eligible post autologous transplant after 100 days post transplant, with recovery of their counts absolute neutrophil count (ANC) \> 1000 and platelets greater than 75K at some point post transplant * Karnofsky performance status \>= 60% * Total bilirubin \< 1.5 x institutional upper limit of normal * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal * Creatinine \< 1.5 x institutional upper limit of normal OR creatinine clearance \>= 60 mL/min for patients with creatinine levels above 1.5 x institutional upper limit of normal * Pregnant women will be excluded from this trial; nursing women are also excluded; women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) for the duration of study participation, and for 3 months after completion of study; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document * Patients should not be receiving any other investigational agents Exclusion Criteria: * Patients with clinically significant illnesses which would compromise participation in the study, including, but not limited to: active or uncontrolled infection, immune deficiencies or confirmed diagnosis of human immunodeficiency virus (HIV) infection, active Hepatitis B, active Hepatitis C, or uncontrolled diabetes, uncontrolled hypertension, symptomatic congestive heart failure, unstable angina pectoris, myocardial infarction within the past 6 months, uncontrolled cardiac arrhythmia; or psychiatric illness/social situations that would limit compliance with study requirements * Patients with additional (other than AML/MDS) currently active primary malignancy other than curatively treated carcinoma in situ (CIS) of the cervix, or basal or squamous cell carcinoma of the skin; patients are not considered to have a "currently active" malignancy if they have completed therapy for a prior malignancy and disease free from prior malignancies for \> 2 years * Patients with active central nervous system (CNS) disease; these patients are excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events * Active infections, including opportunistic following allo, MUD, or auto transplant (including but not limited to cytomegalovirus \[CMV\], fungal infection etc)