Venetoclax, Ponatinib, and Dexamethasone in Participants With Philadelphia Chromosome or BCR-ABL Positive Relapsed or Refractory Acute Lymphoblastic Leukemia or Chronic Myelogenous Leukemia

Inclusion Criteria:

* Patients with relapsed/refractory Ph-positive ALL or lymphoid blast phase CML (either t(9;22) and/or BCR-ABL1 positive by fluorescent in situ hybridization or polymerase chain reaction), including prior therapy with at least one Bcr-Abl tyrosine kinase inhibitor
* Performance status =\< 3 Eastern Cooperative Oncology Group (ECOG scale)
* Total serum bilirubin =\< 1.5 x upper limit of normal (ULN), unless due to Gilbert's syndrome, hemolysis or the underlying leukemia approved by the principal investigator (PI)
* Alanine aminotransferase (ALT) =\< 1.5 x ULN, unless due to the underlying leukemia approved by the PI
* Aspartate aminotransferase (AST) =\< 1.5 x ULN unless due to the underlying leukemia approved by the PI
* Creatinine clearance \>= 30 mL/min
* Serum lipase and amylase =\< 1.5 x ULN
* Ability to swallow
* Signed informed consent

Exclusion Criteria:

* Prior history of treatment with venetoclax. Prior ponatinib is allowed
* Active serious infection not controlled by oral or intravenous antibiotics (e.g. persistent fever or lack of improvement despite antimicrobial treatment)
* History of acute pancreatitis within 1 year of study or history of chronic pancreatitis
* Uncontrolled hypertriglyceridemia (triglycerides \> 450 mg/dL)
* Active secondary malignancy that in the investigator's opinion will shorten survival to less than 1 year
* Active grade III-V cardiac failure as defined by the New York Heart Association criteria
* Clinically significant, uncontrolled, or active cardiovascular disease, specifically including, but not restricted to: any history of myocardial infarction (MI), stroke, revascularization, unstable angina or transient ischemic attack prior to enrollment; left ventricular ejection fraction (LVEF) less than lower limit of normal per local institutional standards prior to enrollment; diagnosed or suspected congenital long QT syndrome; any history of clinically significant atrial or ventricular arrhythmias (such as uncontrolled atrial fibrillation, ventricular tachycardia, ventricular fibrillation, or Torsades de pointes) as determined by the treating physician; prolonged corrected QT interval (QTc) interval on pre-entry electrocardiogram (\> 480 msec) unless corrected after electrolyte replacement; history of venous thromboembolism including deep venous thrombosis or pulmonary embolism within the past 3 months; uncontrolled hypertension (diastolic blood pressure \> 100 mmHg; systolic \> 150 mmHg)
* Patients currently taking drugs that are generally accepted to have a high risk of causing Torsades de Pointes (unless these can be changed to acceptable alternatives)
* Received strong or moderate CYP3A inhibitors or inducers within 3 days of study entry
* Consumed grapefruit, grapefruit products, Seville oranges, or star fruit within 3 days prior to starting venetoclax
* 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. Prior recent treatment with corticosteroids and hydroxyurea is permitted
* 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 throughout the study period. 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. Appropriate birth control will be determined by the treating physician