Clofarabine and Melphalan Before Donor Stem Cell Transplant in Treating Patients With Myelodysplasia, Acute Leukemia in Remission, or Chronic Myelomonocytic Leukemia

Inclusion Criteria: * Patients in 1st or 2nd remission with acute myeloid leukemia (AML) or acute lymphoblastic leukemia (ALL), who are eligible for stem cell transplant. Remission defined as no circulating blasts, \< 5% blasts in the bone marrow, normalization of previously detected cytogenetic abnormalities, no extramedullary disease * High risk myelodysplastic syndrome (MDS) * Intermediate II and high risk by International Prognostic Scoring System (IPSS) * Intermediate, high, or very high by World Health Organization (WHO) classification-based Prognostic Scoring System (WPSS) * Transfusion dependent * Therapy-related MDS or MDS evolved from previous hematological disorder (excepting myelofibrosis) * Patients with chronic myelomonocytic leukemia (CMML) are allowed to be enrolled * Patients with MDS that has evolved to AML must be in remission * Patients must not be eligible for full ablative regimens by the attending physician * Patients with AML or MDS arising from myeloproliferative neoplasm can be enrolled after principal investigator (PI) approval on case to case basis, depends on the spleen size and degree of bone marrow fibrosis * Performance status of \>= 70% on the Karnofsky scale * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control or abstinence) prior to study entry and for six months following duration of study participation; should a woman become pregnant or suspect she is pregnant while participating on the trial, she should inform her treating physician immediately * Bone marrow and peripheral blood studies must be available for confirmation of diagnosis; cytogenetics, flow cytometry, and molecular studies (such as Flt-3 status) will be obtained as per standard practice * Bone marrow aspirates/biopsies should be performed within 28 (+ 4 day window) days from registration to confirm disease remission status * A pretreatment measured creatinine clearance (absolute value) of \>= 60 mL/minute * Patients must have a serum bilirubin =\< 2.0 mg/dl * Patients must have serum glutamic oxaloacetic transaminase (SGOT) and serum glutamate pyruvate transaminase (SGPT) =\< 2.5 times the institutional upper limit of normal * Ejection fraction measured by echocardiogram or multi gated acquisition scan (MUGA) \> 50% * Diffusing capacity of the lung for carbon monoxide (DLCO) or forced expiratory volume in 1 second (FEV1) \> 45% predicted * Availability of a human leukocyte antigen (HLA) matched (6/6) sibling donor or 8/8 matched unrelated donor; Donors with mismatch at HLA-A, HLA-B, HLA-C, and HLA-DR will be reviewed by matched unrelated donor (MUD) committee and allowed if their mismatch with the recipient does not require additional GVHD prophylaxis (other than tacrolimus and sirolimus), donors with mismatch at HLA-DQ or HLA-DPB are eligible; donor evaluation according to City of Hope (COH) standard operating procedure (SOP) * Donor stem cell source can be either peripheral blood or bone marrow * All patients must have a psychosocial evaluation prior to transplant as per COH SOP * All subjects must have the ability to understand and the willingness to sign a written informed consent * ALL or AML patients who received chemotherapy (induction or consolidation) can proceed to transplant once bone marrow cellularity is \> 10 % with no evidence of leukemia Exclusion Criteria: * Patients who have received a prior autologous or allogeneic transplant are excluded * Patients with significant hepatic dysfunction (not meeting liver function tests \[LFT\] eligibility criteria) * Patients with MDS evolved into AML that is not in remission * Patients with acute promyelocytic leukemia * Patients with myeloproliferative neoplasms * Patients with suspected or proven central nervous system (CNS) leukemia; (diagnostic lumbar puncture not required before enrollment) * Uncontrolled intercurrent illness including, but not limited to ongoing or active or poorly controlled infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, poorly controlled pulmonary disease or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant and lactating women are excluded from this study * Patients who do not agree to practice effective forms of contraception * Human immunodeficiency virus (HIV)-positive patients are excluded from this study * Patients are excluded if they are hepatitis B surface antigen (sAg), hepatitis B (Hep B) core antibody (cAb), or hepatitis C (Hep C) positive. Patients with Hepatitis B cAB positive and Hepatitis B PCR negative are eligible if they started prophylactic treatment prior to registration to trial * Patients who have received radiation therapy as part of their leukemia treatment may be ineligible and individual cases must be presented to the study principal investigator (PI) for determination of eligibility * Any psychiatric, social or compliance issues that, in the treating physician's opinion, will interfere with completion of the transplant treatment and follow up * Medical or psychiatric reasons which make the donor unlikely to tolerate or cooperate with filgrastim (G-CSF) therapy or leukapheresis or bone marrow harvest * Known allergies to clofarabine, melphalan, sirolimus or tacrolimus * Patients with other active malignancies (besides AML, ALL, MDS) requiring treatment or where there is concern of progression are ineligible for this study; however, patients with previously treated skin cancer, early stage cervical or prostate cancer may be eligible if there is no evidence of residual disease * Cord blood as a donor source is not acceptable * Subjects, who in the opinion of the investigator, may not be able to comply with the safety monitoring requirements of the study