Prexasertib (LY2606368), Cytarabine, and Fludarabine in Patients With Relapsed or Refractory Acute Myeloid Leukemia or High-Risk Myelodysplastic Syndrome

Inclusion Criteria: * All patients with histologically or cytologically confirmed relapsed or refractory acute myeloid leukemia (AML) (except acute promyelocytic leukemia) or relapsed or refractory high-risk myelodysplastic syndrome (HRMDS) (intermediate 2 \[Int-2\] or higher risk by International Prognostic Scoring System \[IPSS\]); patients with chronic myelomonocytic leukemia (CMML) can be enrolled if they can be classified as HRMDS using MDS criteria; patients should not have received more than one salvage therapy; second induction regimen or stem cell transplant in remission will be considered salvage therapy; refractory subjects, up to second consecutive salvage * Patients must have a performance status of 0-2 (Eastern Cooperative Oncology Group \[ECOG\] scale) * Serum creatinine less than or equal to 1.3 mg/dL and/or creatinine clearance \> 40 mL/min * Bilirubin less than or equal to 1.5 mg/dl (unless due to Gilbert's syndrome) * Serum glutamic-oxaloacetic transaminase (SGOT)/aspartate transaminase (AST) or serum glutamate pyruvate transaminase (SGPT)/alanine transferase (ALT) less than or equal to 2.5 X the upper limit of normal (ULN) for the reference lab * Patients must have normal cardiac ejection fraction (left ventricular ejection fraction \[LVEF\] \>/= 45%) * Corrected QT (QTc) interval =/\< 470 msecs, no familial history of QTc prolongation or ventricular arrhythmias * Female patients must not be pregnant or lactating; female patients of childbearing potential (including those \< 1 year post-menopausal) and male patients must agree to use contraception * Patients who have received prior stem cell transplantation will be allowed to enroll as long as prior transplantation has been at least 3 months before enrollment in the trial and any transplant related toxicities have subsided to grade 1 or less Exclusion Criteria: * Patients must not have untreated or uncontrolled life-threatening infection * Patients must not have been treated with CHK1/2 inhibitors * Patients must not have received chemotherapy and/or radiation therapy within 2 weeks of start of protocol treatment; hydroxyurea is allowed up to 48 hours prior to starting therapy in the setting of rapidly proliferating disease * Patients must not have received an investigational anti-cancer drug within two weeks of start of protocol treatment * Patients must not have active central nervous system leukemia; patients with history of central nervous system (CNS) leukemia with no evidence of active CNS disease may be enrolled; maintenance intrathecal chemotherapy for adequately treated CNS involvement with leukemia is allowed with approval from the study supporter * Patients must not have significant cardiac co-morbidity including: history of acute coronary syndromes (including myocardial infarction and unstable angina) within 12 months; coronary angioplasty or stenting within 6 months; history or evidence of current \>/= class III congestive heart failure as defined by the New York Heart Association (NYHA); patients with intra-cardiac defibrillators or permanent pacemakers