Veliparib and Temozolomide in Treating Patients With Acute Leukemia

Inclusion Criteria: * Histologically or cytologically confirmed diagnosis of one of the following: * Relapsed or refractory acute myeloid leukemia (AML); patients with acute promyelocytic leukemia t(15;17) must have failed tretinoin (ATRA), arsenic, and gemtuzumab ozogamycin to be eligible (patients should be refractory to all three agents-absence of durable hematologic response or relapse with complete remission \[CR\] duration of less than 6 months) * Relapsed or refractory pre-B- or T-cell acute lymphoblastic leukemia (ALL); patients with Philadelphia chromosome-positive (Ph+) ALL \[t(9;22)\] will be eligible provided that they have failed (intolerance/resistance) at least 2 different tyrosine kinase inhibitors (TKIs) or have a mutation associated with resistance to TKIs (T315I) * Chronic myelogenous leukemia (CML) in accelerated or blastic phase; patients failed (resistance/intolerance) at least 2 different TKIs or have a mutation associated with resistance to TKIs (T315I) * Chronic myelomonocytic leukemia-2 (CMML-2) defined as having \> 10% blasts (including promonocytes) in the bone marrow or \> 5-19% blasts (including promonocytes) in the peripheral blood * AML arising in the setting of antecedent myelodysplasia (MDS) or myeloproliferative disorder (MPD) * Therapy-related AML * Untreated AML in adults 60 years of age and older who are not candidates for induction chemotherapy due to poor-risk features including adverse cytogenetics or molecular markers (fms-related tyrosine kinase 3 \[FLT3\] internal tandem duplication \[ ITD\]+), or are unwilling to receive intensive induction chemotherapy; adverse cytogenetics: complex karyotype (\>= 3 chromosomal abnormalities), 5q-, 7q-, 9q-, 20q-, abn12p, +21, +8, t(6;9), t(6;11), t(11;19), -7, -5, inv3/t(3;3), abn11q23, abn17p, abn21q * Untreated ALL in adults 60 years of age and older who are not candidates for induction chemotherapy due to poor-risk features including adverse cytogenetics \[t(4;11); t(1;19), hypodyploidy\] or are unwilling to receive intensive induction chemotherapy; patients with Ph+ ALL \[t(9;22)\] will be eligible provided that they have failed (intolerance/resistance) at least 2 different TKIs or have a mutation associated with resistance to TKIs (T315I) * Previous therapy * Only patients who have received or are ineligible for established curative regimens, including stem cell transplantation when applicable, can be enrolled on this study * Patients may have received any number of prior chemotherapy regimens, which may include allogeneic or autologous transplantation, provided that performance status and organ function are maintained * Previous cytotoxic chemotherapy should have been completed at least 3 weeks and radiotherapy at least 2 weeks prior to treatment on the study (6 weeks if the last regimen included carmustine \[BCNU\] or mitomycin C) and all adverse events (excluding alopecia, acne, rash) due to agents administered more than 3 weeks earlier should recover to =\< grade 1; patients with hematologic malignancies are expected to have hematologic abnormalities at study entry; these abnormalities which are thought to be primarily related to the underlying leukemia, are not considered to be toxicities (AE) and do not need to resolve to =\< grade 1 * Patients should stop taking all biologic agents including hematopoietic growth factors, imatinib or similar TKIs, at least 1 week prior to treatment on the study and all adverse events (excluding alopecia, acne, rash) due to agents administered more than 1 week earlier should recover to =\< grade 1; since only patients with advanced Ph+ ALL and CML in accelerated/blast phase are eligible for this study, this short period off TKIs was selected to avoid rapid leukemia progression; if using hydroxyurea, corticosteroids, or leukopheresis for blast count control, patients must be off \>= 24 hrs before starting treatment on the study * Patients who have undergone autologous stem cell transplantation (ASCT) are eligible provided that they are \>= 4 weeks from stem cell infusion and meet other eligibility criteria * Patients who have undergone allogeneic SCT (alloSCT) are eligible if they are \>= 60 days post stem cell infusion, have no evidence of graft vs. host disease, and are \>= 2 weeks off all immunosuppressive therapy * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Patients have to be able to swallow pills * Total or direct bilirubin \< 2 mg/dl * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) \< 5 X institutional upper limit of normal * Creatinine \< 2 mg/dl * Female patients of childbearing potential must have a negative pregnancy test * Female patients of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 30 days afterward; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients may not be receiving any other investigational agents, or concurrent chemotherapy, radiation therapy, or immunotherapy * Any previous treatment with temozolomide * Patients with active central nervous system leukemia are excluded from this clinical trial because they may develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events; patients with a history of central nervous system (CNS) leukemia but no active disease at the time of enrollment are eligible * Hyperleukocytosis with \> 30,000 blasts/ul; (if using hydroxyurea, corticosteroids, or leukopheresis for blast count control, patients must be off \>= 24 hrs before starting treatment on the study); once patient starts treatment on the study the hydroxyurea use should be avoided, however, for patients with rapidly proliferating disease use of hydroxyurea is allowed on treatment days 1 through 12 if it becomes necessary to control a rising white blood cell (WBC) or leukostasis; the WBC need not reach 30,000/ul to start hydroxyurea during protocol days 1-12; the decision to start hydroxyurea during this time is at the discretion of the treating physician * History of allergic reactions attributed to compounds of similar chemical or biologic composition to ABT-888 or temozolomide used in this study * Active, uncontrolled infection; patients with infection under active treatment and controlled with antibiotics are eligible * Uncontrolled intercurrent illness including, but not limited to, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with ABT-888 * Known human immunodeficiency virus (HIV) infected patients (HIV testing will not be performed as a part of screening) on combination antiretroviral therapy, exclusive of zidovudine or starvudine, or HIV infected patients not on or willing to suspend antiretroviral therapy will be eligible provided that their cluster of differentiation (CD)4 cell count is greater than 250/mm3; HIV infected patients with CD4 count equal or less than 250/mm3 will be excluded