Entinostat and Clofarabine in Treating Patients With Newly Diagnosed, Relapsed, or Refractory Poor-Risk Acute Lymphoblastic Leukemia or Bilineage/Biphenotypic Leukemia

Inclusion Criteria: * Adults age \>= 40 years with the established, pathologically-confirmed diagnoses of newly diagnosed ALL or ABL are eligible for study; adults with relapsed and refractory ALL or ABL who are \>= 21 years of age and who have progressive disease following their last therapy are eligible for study; the additional following criteria must be met: * For adults with relapsed/refractory ALL, no more than 5 previous regimens * Eastern Cooperative Oncology Group (ECOG) performance status 0, 1, or 2 * Patients must be able to give informed consent * Female patients of childbearing age must have negative pregnancy test * Total white blood cell count (WBC) =\< 150,000 with no evidence for ongoing or impending leukostasis * Total bilirubin =\< 2.0 mg/dL unless elevated due to Gilbert's disease, hemolysis or leukemic infiltration * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 2.5 × upper limit of normal (ULN) unless due to leukemic infiltration * Serum creatinine =\< 2.0 mg/dL * Left ventricular ejection fraction (LVEF) \>= 45% as measured by echocardiogram (ECHO) or multi gated acquisition (MUGA) scan * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for 30 days after study participation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediatel…