Selinexor With Fludarabine and Cytarabine for Treatment of Refractory or Relapsed Leukemia or Myelodysplastic Syndrome

Inclusion Criteria: * Participants must have a diagnosis of AML, MDS, ALL or MPAL and must have disease that has relapsed or is refractory to chemotherapy, or that has relapsed after hematopoietic stem cell transplantation (HSCT) * Refractory disease is defined as persistent disease after at least two courses of induction chemotherapy. * Patients with AML, MPAL or MDS are eligible at first or subsequent relapse, whereas patients with ALL are eligible at second or subsequent relapse or any relapse that is refractory to salvage chemotherapy. * Patients with AML or ALL must have ≥ 5% leukemic blasts in the bone marrow or increasing levels of MRD in the bone marrow as assessed by flow cytometry. If an adequate bone marrow sample cannot be obtained, patients may be enrolled if there is unequivocal evidence of leukemia in the peripheral blood. * Adequate organ function defined as the following: * Direct bilirubin ≤ 1.5 x institutional upper limit of normal (IULN) * AST (SGOT)/ALT (SGPT) \< 3 x IULN * Creatinine within normal institutional limits for age * Prothrombin time (PT) and partial thromboplastin (PTT) ≤ 1.5 x IULN. * Age criteria: Patients treated at collaborating sites and current St. Jude patients who are on therapy or within 3 years of completion of therapy must be ≤ 24 years old. All other St. Jude patients must be \< 21 years old. * Patients must be able to swallow tablets. * Performance status: Lansky ≥ 50 for patients who are ≤ 16 years old and Karnofsky ≥ 50% for patients who are \> 16 years old. * Patients must have fully recovered from the acute effects of all prior therapy. * For patients who have received prior HSCT, there can be no evidence of GVHD and greater than 60 days must have elapsed since the HSCT. Exclusion Criteria: * History of cerebellar toxicity or cerebellar neurological findings on exam. * Must not be pregnant or breastfeeding. Female patients of child-bearing potential must agree to use dual methods of contraception and have a negative serum pregnancy test at screening, and male patients must use an effective barrier method of contraception if sexually active with a female of child-bearing potential. Acceptable methods of contraception are condoms with contraceptive foam, oral, implantable or injectable contraceptives, contraceptive patch, intrauterine device, diaphragm with spermicidal gel, or a sexual partner who is surgically sterilized or post-menopausal. For both male and female patients, effective methods of contraception must be used throughout the study and for three months following the last dose. * Patients with Down syndrome, acute promyelocytic leukemia, juvenile myelomonocytic leukemia, Fanconi anemia, Kostmann syndrome, Shwachman syndrome, or other bone marrow failure syndromes are not eligible. * Use of investigational agents, with the exception of gemtuzumab ozogamicin, within 30 days. * Any significant concurrent disease, illness, or psychiatric disorder that would compromise patient safety or compliance, study participation, follow up, or interpretation of study research. * Unstable cardiovascular function: * symptomatic ischemia * congestive heart failure NYHA Class \> 3 * myocardial infarction (MI) within 3 months * Uncontrolled infection requiring parenteral antibiotics, antivirals, or antifungals within one week prior to first dose. Infections controlled on concurrent anti-microbial agents are acceptable, and anti-microbial prophylaxis per institutional guidelines are acceptable. * Known human immunodeficiency virus (HIV) infection (pre-study testing not required). * Patients with malabsorption syndrome, or any other disease significantly affecting gastrointestinal function. * Prior treatment with selinexor.