Navitoclax in Relapsed or Refractory High-Risk Myelodysplastic Syndrome

Inclusion Criteria: * Provide signed and dated informed consent form * Willing to comply with all study procedures and be available for the duration of the study * Male or female, aged 18 years or older * Must have myelodysplastic syndrome with Revised International Prognostic Score (IPSS-R) of at least 3 and have been previously treated with hypomethylating agent (HMA) (azacitidine or decitabine) and venetoclax for at least 2 cycles. Patients in the phase I portion of the trial may be enrolled if they have not received venetoclax with HMA therapy * Prior hematopoietic stem cell transplant will be allowed if 90 or more days has passed since the date of transplant to day 1 of cycle 1 and patients are no longer taking immunosuppressive agents * Eastern Cooperative Oncology Group (ECOG) Performance Status of 0-2 * Must be able to swallow pills whole * Creatinine clearance \>= 40 mL/min, calculated with the use of the 24-hour creatinine clearance or modified Cockcroft-Gault equation * Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) =\< 2.5 x upper limit of normal (ULN) * Total bilirubin =\< 1.5 x ULN (or =\< 3 x ULN for patients with documented Gilbert syndrome) * Coagulation: activated partial thromboplastin time (aPTT) and international normalized ratio (INR) =\< 1.5 x ULN * A female participant is eligible to participate if she is not pregnant, not breastfeeding, and at least one of the following conditions applies: * Not a woman of childbearing potential (WOCBP) * A WOCBP who agrees to follow contraceptive guidance during the treatment period and for at least 120 days after the last dose of study treatment. Approved methods are detailed below * Hormonal Methods: levonorgestrel-releasing intrauterine system (e.g., Mirena, registered trademark), implants, hormone shot or injection, combined pill, minipill, patch * If not surgically sterile, male patients must be willing to practice at least one of the following highly effective methods of birth control for at least their partner's menstrual cycle before and for 120 days after study drug administration.Surgically sterile male patients may practice birth control measures at their own discretion * Two of the following barrier/intrauterine methods: * Male or female condom with or without spermicide, cap, diaphragm, or sponge with spermicide, copper T intrauterine device * Hormonal methods * Levonorgestrel-releasing intrauterine system (e.g., Mirena) implants * Hormone shot or injection * Combined pill * Minipill * Patch * Barrier/intrauterine methods combined with hormonal methods Exclusion Criteria: * Active, uncontrolled systemic infection. Patients on prophylactic antibiotics are NOT excluded * Uncontrolled human immunodeficiency virus (HIV), hepatitis B virus (HBV), or hepatitis C virus (HCV) infections defined as detectable viral load * History of any active malignancy within the past 2 years prior to screening, with the exception of: * Adequately treated carcinoma in situ of the uterine cervix * Adequately treated basal cell carcinoma or localized squamous cell carcinoma of the skin * Asymptomatic prostate * Subject requiring a medication that interferes with coagulation or platelet function - except for low dose aspirin (up to 100 mg daily) and prophylactic dose low molecular weight heparin (LMWH). Subjects prescribed these medications prior to enrollment should discontinue at least 3 days prior to C1D1. If they are not able to discontinue these medications, subjects will be excluded * White blood cells (WBC) \> 25,000 cells/microL. Hydroxyurea therapy to reduce WBC count prior to enrollment is NOT excluded * Malabsorption syndrome or other condition precluding enteral medication administration * Subjects treated concomitantly with CYP2C8 substrates, CYP2C9 substrates, CYP3A inhibitors, CYP3A inducers and P-glycoprotein inhibitors are allowed. Venetoclax dosing must be adjusted. Pregnancy or lactation or intending to become pregnant during the study * Pregnancy or lactation or intending to become pregnant during the study * Known allergic reactions to components of the study product(s) * Treatment with another investigational drug or other intervention within 2 weeks of planned cycle 1 day 1 (C1D1)