Low-Intensity Chemotherapy and Venetoclax in Treating Patients With Relapsed or Refractory B- or T-Cell Acute Lymphoblastic Leukemia

Inclusion Criteria: 1. Diagnosis of one of the following 1. Patients ≥ 18 years of age with relapsed/refractory B- or T-cell ALL (for phase II only) 2. Patients ≥ 60 years of age with previously untreated B- or T-cell ALL. Patients \<60 years of age may be enrolled if they are considered unfit for intensive chemotherapy 3. Patients ≥ 60 years of age with previously treated B- or T-cell ALL who received 1-2 courses of any frontline chemotherapy. Patients \<60 years of age may be enrolled if they are considered unfit for intensive chemotherapy * If they achieved CR/CRi, they are assessable only for event-free and overall survival * If they failed to achieve CR/CRi, they are assessable for response, event-free, and overall survival 2. Performance status ≤ 3 (Eastern Cooperative Oncology Group \[ECOG\] Scale) 3. Adequate liver and renal function as defined by the following criteria: * Total serum bilirubin ≤ 1.5 x upper limit of normal (ULN) * Alanine aminotransferase (ALT) ≤ 3 x ULN, unless due to disease involvement of the liver or hemolysis, in which case an ALT ≤ 10 x ULN is acceptable * Aspartate aminotransferase (AST) ≤ 3 x ULN, unless due to disease involvement of the liver or hemolysis, in which case an ALT ≤ 10 x ULN is acceptable * Creatinine clearance ≥ 30 mL/min * INR ≤ 1.5 x ULN and aPTT . 1.5 x ULN 4. For females of childbearing potential, a negative pregnancy test must be documented within 1 week of starting treatment 5. Female and male patients who are fertile must agree to use an effective form of contraception (birth control methods while on study, such as birth control pills or injections, intrauterine devices \[IUDs\]), or double-barrier methods (for example, a condom in combination with spermicide) with their sexual partners for 4 months after the end of treatment 6. Signed informed consent Exclusion Criteria: 1. Patients with Philadelphia chromosome-positive ALL or Burkitt leukemia 2. Patients who are willing and eligible to receive intensive chemotherapy (only for patients enrolling in frontline cohort) 3. Active serious infection not controlled by oral or intravenous antibiotics 4. Known CNS leukemia requiring radiation 5. Active GVHD 6. Active secondary malignancy other than skin cancer (e.g., basal cell carcinoma or squamous cell carcinoma) that in the investigator's opinion will shorten survival to less than 1 year 7. Known hepatitis B or C infection, or known seropositivity for human immunodeficiency virus (HIV) 8. Active grade III-V cardiac failure as defined by the New York Heart Association Criteria 9. Patients with a cardiac ejection fraction (as measured by either multigated acquisition \[MUGA\] or echocardiogram) \< 40% 10. Received moderate or strong CYP3A inhibitors or strong CYP3A inducers within 7 days of starting venetoclax 11. Received medication that interferes with coagulation or platelet function within 7 days prior to the first dose of study drug or during the study treatment period 12. Consumed grapefruit, grapefruit products, Seville oranges, or star fruit within 3 days prior to starting venetoclax 13. Prior history of treatment with navitoclax. 14. Treatment with any investigational antileukemic agents or chemotherapy agents in the last 7 days before study entry, unless full recovery from side effects has occurred or patient has rapidly progressive disease judged to be life-threatening by the investigator. Exception: Treatment with hydroxyurea and/or dexamethasone are allowed prior to study treatment, without window of exclusion 15. Pregnant and lactating women will not be eligible; women of childbearing potential should have a negative pregnancy test prior to entering on the study and be willing to practice methods of contraception. Women do not have childbearing potential if they have had a hysterectomy or are postmenopausal without menses for 12 months. In addition, men enrolled on this study should understand the risks to any sexual partner of childbearing potential and should practice an effective method of birth control 16. History of significant bleeding disorder unrelated to cancer, including: diagnosed congenital bleeding disorders (e.g., von Willebrand's disease); diagnosed acquired bleeding disorder within one year (e.g., acquired anti-factor VIII antibodies) 17. Patient with total serum bilirubin \> 1.5 x upper limit of normal (ULN).