• Documented informed consent of the participant and/or legally authorized representative

• Karnofsky performance status \>= 70

• Histologically confirmed diagnosis of one the following:

‣ Patients with acute myelogenous leukemia

• In first complete remission (CR1) with intermediate or poor risk cytogenetics according to National Comprehensive Cancer Network (NCCN) guidelines for acute myeloid leukemia (AML) or European LeukemiaNet (ELN) 2017

∙ In second complete remission (CR2) or third complete remission (CR3)

∙ Patients with chemosensitive active disease

⁃ Patients with acute lymphocytic leukemia

• In CR1 with poor risk cytogenetics:

⁃ For adults according to NCCN guidelines for acute lymphoblastic leukemia (ALL): Patients older than 40 year of age; with high white blood cell count (WBC) at diagnosis (\>= 30,000 for B lineage or \>= 50,000 for T lineage), or with high risk cytogenetics including: hypoploidy (\< 44 chromosomes); t(v;11q23): MLL rearranged; t(9;22) (q34;q11.2); complex cytogenetics (5 or more chromosomal abnormalities)

⁃ For pediatrics t(9;22), iAMP21loss of 13q, and abnormal 17p

• In CR2 or CR3

∙ Patients with chemosensitive active disease

⁃ Myelodysplastic syndrome in high-intermediate (int-2) and high risk categories by International Prognostic Scoring System (IPSS) or revised (R)-IPSS

• Total bilirubin =\< 2 X upper limit of normal (ULN) (unless has Gilbert's disease) (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated)

• Creatinine clearance of \>= 60 mL/min per 24 hour urine test or the Cockcroft-Gault formula (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated)

• Ejection fraction measured by echocardiogram or multigated acquisition scan (MUGA) \>= 50% (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated)

‣ Note: To be performed within 28 days prior to day 1 of protocol therapy

• If able to perform pulmonary function tests: forced expiratory volume in 1 second (FEV1), forced vital capacity (FVC) and carbon monoxide diffusing capability test (DLCO) (diffusion capacity) \>= 50% of predicted (corrected for hemoglobin). If unable to perform pulmonary function tests: oxygen (O2) saturation \> 92% on room air

‣ Note: To be performed within 28 days prior to day 1 of protocol therapy

• Seronegative for human immunodeficiency virus (HIV) antigen (Ag)/antibody (Ab) combo, hepatitis C virus (HCV), active hepatitis B virus (HBV) (surface antigen negative), and syphilis (rapid plasma reagin \[RPR\]) (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated)

‣ If positive, hepatitis C ribonucleic acid (RNA) quantitation must be performed

• Meets other institutional and federal requirements for infectious disease titer requirements

‣ Note: Infectious disease testing to be performed within 28 days prior to Day 1 of protocol therapy

• Women of childbearing potential (WOCBP): negative urine or serum pregnancy test

‣ If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required

• Agreement by females and males of childbearing potential\* to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 6 months after the last dose of protocol therapy

‣ Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only)

• The recipient must have a related donor genotypically human leukocyte antigen (HLA)-A, B,C and DRB1 loci haploidentical to the recipient

• No HLA matched sibling or matched unrelated donor is available

• Patients should be off all previous intensive therapy, chemotherapy or radiotherapy for 3 weeks prior to commencing therapy on this study

‣ (NOTE: Low dose chemotherapy or maintenance chemotherapy given within 7 days of planned study enrollment is permitted. These include: Hydroxyurea, 6-meraptopurine, oral methotrexate, vincristine, oral etoposide, and tyrosine kinase inhibitors \[TKIs\]. FLT-3 inhibitors such as sorafenib, crenolanib, midostaurin can also be given up to 3 days before conditioning regimen.)

• DONOR: The donor must be examined and have specific tests performed according to existing institutional guidelines to evaluate his/her candidacy as a donor including the following:

• DONOR: Age =\< 60 years of age

• DONOR: For younger donors, no more than 20 mL bone marrow may be harvested per kg of donor body weight

• DONOR: Medical history and physical examination confirm good health status as defined by institutional standards

• DONOR: Seronegative for HIV Ag, HIV 1+2 Ab, HTLV I/II Ab, hepatitis B surface antigen (HBsAg), hepatitis B core antibody (HBcAb) (IgM and IgG), HCV Ab, RPR for syphilis within 30 days of apheresis collection

• DONOR: Genotypically haploidentical as determined by HLA typing, preferably a nonmaternal HLA haploidentical relative due to data of high incidence of graft failure with use of maternal HLA haploidentical cells. Eligible donors include biological parents, siblings or half siblings, or children

• DONOR: Female donors of child-bearing potential must have a negative serum or urine beta-human chorionic gonadotropin (HCG) test within seven days of mobilization

• DONOR: The donor must have been informed of the investigational nature of this study and have signed a consent form in accordance with Federal Guidelines and the guidelines of the participating institution

• DONOR: Selection of a haploidentical donor will require absence of pre-existing donor-directed anti-HLA antibodies in the recipient