Fludarabine, Cytarabine, and Pegcrisantaspase for the Treament of Relapsed or Refractory Leukemia

Inclusion Criteria: * Patients with a diagnosis of relapsed or refractory leukemia including, but not limited to acute myeloid leukemia (AML), acute lymphoblastic leukemia (ALL), T-cell prolymphocytic leukemia, biphenotypic acute leukemia, or blast-phase of chronic myeloid Leukemia (CML) will be allowed during the safety lead-in phase * For cohort A of the expansion phase: Patients with a diagnosis untreated adverse-risk AML (as defined by ELN \[European Leukemia Net Classification\] 2017) will be enrolled * For cohort B of the expansion phase: Patients with a diagnosis of relapsed or refractory AML will be enrolled * Bilirubin =\< 2 mg/dL * Aspartate aminotransferase (AST) and/or alanine aminotransferase (ALT) =\< 2.5 x upper limit of normal (ULN) * Creatinine =\< 1.5 x ULN * Cardiac ejection fraction of \> or = 45% within the past 3 months * Amylase and lipase =\< 1.5 x ULN * Eastern Cooperative Oncology Group (ECOG) performance status of =\< 2 * A negative urine pregnancy test is required within one week (7 days) for all women of childbearing potential prior to being registered on this trial * Patient must have the ability to understand the requirements of the study and signed informed consent. A signed informed consent by the patient or his legally authorized representative is required prior to their enrollment on the protocol Exclusion Criteria: * Pregnant women are excluded from this study because the agents used in this study have the potential for teratogenic or abortifacient effects. Because there is a potential risk for adverse events in nursing infants secondary to treatment of the mother with the chemotherapy agents, breastfeeding should also be avoided * Uncontrolled intercurrent illness including, but not limited to active uncontrolled infection, symptomatic congestive heart failure (New York Heart Association \[NYHA\] class III or IV), unstable angina pectoris, clinically significant cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Patient with documented hypersensitivity to any of the components of the chemotherapy program * Prior treatment with pegylated asparaginase * Patients with a diagnoses of acute promyelocytic leukemia (AML-M3) will be excluded from this trial * Men and women of childbearing potential who do not practice contraception. Women of childbearing potential and men must agree to use contraception prior to study entry and for the duration of study participation. Effective methods of birth control include: * Birth control pills, shots, implants or patches * Intrauterine devices (IUDs) * Condom or occlusive cap (diaphragm or cervical/vault caps) used with spermicide * Abstinence * Females of non-childbearing potential are those who are postmenopausal greater than 1 year or who have had a bilateral tubal ligation, oophorectomy, and/or hysterectomy * Patients with history of clinically significant venous thromboembolism