Pevonedistat, Azacitidine, Fludarabine Phosphate, and Cytarabine in Treating Patients With Relapsed or Refractory Acute Myeloid Leukemia or Myelodysplastic Syndrome

Inclusion Criteria

• •Patients must have had histologic verification of AML at the original diagnosis. Patients must have one of the following:
• •* Recurrent disease in \>= 1st relapse with \>= 5% blasts in the bone marrow (M2/M3) marrow OR immunophenotypic evidence of disease with \>= 0.1% blasts detected by flow cytometry, OR evidence of recurrent cytogenetic or molecular abnormalities consistent with relapse, with or without extramedullary disease
• •* Refractory AML is defined as \>= 5% blasts in the bone marrow (M2/M3) after \>= 2 induction attempts (i.e., 2 cycles of chemotherapy)
• •* Patients with advanced MDS, including MDS that has progressed to AML, and have experienced relapse or are refractory after \>= 1 course of induction therapy, are eligible
• •Karnofsky \>= 50% for patients \> 16 years of age and Lansky \>= 50 for patients =\< 16 years of age
• •Patients must have fully recovered from the acute toxic effects of all prior anti-cancer therapy and must meet the following minimum duration from prior anti-cancer directed therapy prior to enrollment. If after the required timeframe, the numerical eligibility criteria are met, e.g., blood count criteria, the patient is considered to have recovered adequately
• •* Cytotoxic chemotherapy or other anti-cancer agents known to be myelosuppressive
• •* \>= 14 days must have elapsed after the completion of other cytotoxic therapy, with the exception of hydroxyurea, for patients not receiving standard maintenance therapy. Additionally, patients must have recovered from all acute toxic effects of prior therapy
• •* NOTE: Cytoreduction with hydroxyurea must be discontinued \>= 24 hours prior to the start of protocol therapy
• •* Anti-cancer agents not known to be myelosuppressive (e.g. not associated with reduced platelet or absolute neutrophil \[ANC\] counts): \>= 7 days after the last dose of agent
• •* Antibodies: \>= 21 days must have elapsed from infusion of last dose of antibody, and toxicity related to prior antibody therapy must be recovered to grade =\< 1
• •* Hematopoietic growth factors: \>= 14 days after the last dose of a long-acting growth factor (e.g. pegfilgrastim) or 7 days for short-acting growth factor. For agents that have known adverse events occurring beyond 7 days after administration, this period must be extended beyond the time during which adverse events are known to occur. The duration of this interval must be discussed with the study chair and the study-assigned research coordinator
• •* Interleukins, interferons and cytokines (other than hematopoietic growth factors): \>= 21 days after the completion of interleukins, interferon or cytokines (other than hematopoietic growth factors)
• •* Stem cell Infusions (with or without traumatic brain injury \[TBI\]):
• •* Allogeneic (non-autologous) bone marrow or stem cell transplant, or any stem cell infusion including donor leukocyte infusion (DLI) or boost infusion: \>= 84 days after infusion and no evidence of graft versus host disease (GVHD)
• •* Autologous stem cell infusion including boost infusion: \>= 42 days
• •* Cellular Therapy: \>= 30 days after the completion of any type of cellular therapy (e.g. modified T cells, natural killer \[NK\] cells, dendritic cells, etc.)
• •* Radiation therapy (XRT)/external beam irradiation including protons: \>= 14 days after local XRT; \>= 42 days after TBI, craniospinal XRT or if radiation to \>= 50% of the pelvis; \>= 42 days if other substantial brain metastases (BM) radiation
• •* Radiopharmaceutical therapy (e.g., radiolabeled antibody, 131 iodine \[I\]-metaiodobenzylguanidine \[MIBG\]): \>= 42 days after systemically administered radiopharmaceutical therapy
• •* Patients must not have received prior exposure to MLN4924 (pevonedistat)
• •Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 60 ml/min/1.73 m\^2 or a serum creatinine based on age/gender as follows:
• •* 1 month to \< 6 months; 0.4 (male and female)
• •* 6 months to \< 1 year; 0.5 (male and female)
• •* 1 to \< 2 years; 0.6 (male and female)
• •* 2 to \< 6 years; 0.8 (male and female)
• •* 6 to \< 10 years; 1 (male and female)
• •* 10 to \< 13 years; 1.2 (male and female)
• •* 13 to \< 16 years; 1.5 (male) and 1.4 (female)
• •* \>= 16 years; 1.7 (male) and 1.4 (female)
• •Bilirubin (sum of conjugated + unconjugated) =\< upper limit of normal (ULN) for age
• •Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 x ULN. For the purpose of this study, the ULN for serum glutamate pyruvate transaminase (SGPT) is 45 U/L
• •Shortening fraction of \>= 27% by echocardiogram, or
• •Ejection fraction of \>= 50% by echocardiogram or radionuclide angiogram
• •No ventricular or supraventricular arrhythmia on electrocardiogram (EKG)
• •Prolonged rate corrected QT (QTc) interval \< 500 msec
• •Pulse oximetry \> 94% on room air if there is clinical indication for determination (e.g. dyspnea at rest)
• •International normalized ratio (INR) =\< 1.5
• •Hemoglobin \> 8.0 g/dL (may receive red blood cell \[RBC\] transfusions)
• •All patients and/or their parents or legally authorized representatives must sign a written informed consent. Assent, when appropriate, will be obtained according to institutional guidelines