Talazoparib and Temozolomide in Treating Younger Patients With Refractory or Recurrent Malignancies

Inclusion Criteria: * Age: * Phase 1 (Part A) * Patients must be \> than 12 months and =\< 21 years of age at the time of study enrollment * Phase 2 (Part B) * Patients must be \> than 12 months and =\< 30 years of age at the time of study enrollment * Body surface area (for Parts A and B): * Patients must have a body surface area (BSA) of \>= 0.42 m\^2 at the time of study enrollment * Diagnosis: * Phase 1 (Part A) * Solid tumors (Part A1): patients with relapsed or refractory solid tumors including central nervous system (CNS) tumors without bone marrow involvement are eligible; patients must have had histologic verification of malignancy at original diagnosis or relapse except in patients with intrinsic brain stem tumors, optic pathway gliomas, or patients with pineal tumors and elevations of cerebrospinal fluid (CSF) or serum tumor markers including alpha-fetoprotein or beta-human chorionic gonadotropin (HCG) * Ewing sarcoma or peripheral primitive neuroectodermal tumor (PNET) (Part A2): patients with relapsed or refractory Ewing sarcoma or peripheral PNET without bone marrow involvement will be eligible for Part A2 if there are no available slots on Part A1; these patients will be enrolled at one dose level below the dose level at which patients on Part A1 are actively enrolling, or at the starting dose level (dose level 1) if dose escalation has not yet occurred; patients must have had histologic verification of malignancy at original diagnosis or relapse * Phase 2 (Part B) * Ewing sarcoma or peripheral PNET: patients with relapsed or refractory Ewing sarcoma or peripheral PNET are eligible; patients must have had histologic verification of malignancy at original diagnosis or relapse * Phase 2 (Part C) * Disease status: * Phase 1 (Part A): * Patients must have either measurable or evaluable disease * Phase 2 (Part B): * Ewing sarcoma or peripheral PNET: patients must have measurable disease * Therapeutic options: patient's current disease state must be one for which there is no known curative therapy or therapy proven to prolong survival with an acceptable quality of life * Karnofsky \>= 50% for patients \> 16 years of age and Lansky \>= 50 for patients =\< 16 years of age; Note: neurologic deficits in patients with CNS tumors must have been relatively stable for at least 7 days prior to study enrollment; patients who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score * Patients who have received prior therapy with a temozolomide-based regimen are eligible; Note: patients who have progressed on a poly adenosine diphosphate ribose polymerase (PARP) inhibitor and temozolomide regimen are not eligible for Part A of the study * Patients must have fully recovered from the acute toxic effects of all prior anti-cancer chemotherapy * Myelosuppressive chemotherapy: * Solid tumors (Part A and Part B): at least 21 days after the last dose of myelosuppressive chemotherapy (42 days if prior nitrosourea) * Hematopoietic growth factors: at least 14 days after the last dose of a long-acting growth factor (e.g. Neulasta) or 7 days for short-acting growth factor; for agents that have known adverse events occurring beyond 7 days after administration, this period must be extended beyond the time during which adverse events are known to occur; the duration of this interval must be discussed with the study chair * Biologic (anti-neoplastic agent): at least 7 days after the last dose of a biologic agent; for agents that have known adverse events occurring beyond 7 days after administration, this period must be extended beyond the time during which adverse events are known to occur; the duration of this interval must be discussed with the study chair * Immunotherapy: at least 42 days after the completion of any type of immunotherapy, e.g. tumor vaccines * Monoclonal antibodies: at least 3 half-lives of the antibody after the last dose of a monoclonal antibody * Radiation therapy (XRT): at least 14 days after local palliative XRT (small port); at least 42 days must have elapsed if other substantial bone marrow (BM) radiation; patients with prior total body irradiation (TBI), craniospinal XRT and/or \>= 50% radiation of the pelvis are not eligible * Stem cell infusion without TBI: no evidence of active graft vs. host disease and at least 84 days must have elapsed after transplant or stem cell infusion * PARP inhibitor exposure: * Part A: Patients who have received prior therapy with a PARP inhibitor, with the exception of BMN 673, are eligible; however, patients who have progressed on a PARP inhibitor and temozolomide regimen are not eligible * Part B: Patients who have previously been exposed to a PARP inhibitor are not eligible * For patients with solid tumors without known bone marrow involvement: peripheral absolute neutrophil count (ANC) \>= 1000/mm\^3 * For patients with solid tumors without known bone marrow involvement: platelet count \>= 100,000/mm\^3 (transfusion independent, defined as not receiving platelet transfusions for at least 7 days prior to enrollment) * For patients with solid tumors without known bone marrow involvement: hemoglobin \>= 8.0 g/dL (may receive red blood cell \[RBC\] transfusions) * All patients enrolled on Part A of the study must be evaluable for hematologic toxicity * Patients on Part B of the study with known bone marrow metastatic disease will be eligible for the study provided they meet the blood counts (may receive transfusions provided they are not known to be refractory to red cell or platelet transfusions); these patients will not be evaluable for hematologic toxicity * Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70 ml/min/1.73 m\^2 or a maximum serum creatinine (mg/dL) based on age/gender as follows: * 1 to \< 2 years: 0.6 * 2 to \< 6 years: 0.8 * 6 to \< 10 years: 1 * 10 to \< 13 years: 1.2 * 13 to \< 16 years: 1.5 for males, 1.4 for females * \>= 16 years: 1.7 for males, 1.4 for females * Patients on Part A and Part B: bilirubin (sum of conjugated + unconjugated) =\< 1.5 x upper limit of normal (ULN) for age * Patients on Part A and Part B: serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 110 U/L; for the purpose of this study, the ULN for SGPT is 45 U/L * Patients on Part A and Part B: serum albumin \>= 2 g/dL * All patients and/or their parents or legally authorized representatives must sign a written informed consent; assent, when appropriate, will be obtained according to institutional guidelines * For patients enrolling on Part B: tissue blocks or slides must be sent; if tissue blocks or slides are unavailable, the Study Chair must be notified prior to enrollment Exclusion Criteria: * Pregnant or breast-feeding women will not be entered on this study; pregnancy tests must be obtained in girls who are post-menarchal; males or females of reproductive potential may not participate unless they have agreed to use an effective contraceptive method * Patients receiving corticosteroids who have not been on a stable or decreasing dose of corticosteroid for at least 7 days prior to enrollment are not eligible * Patients who are currently receiving another investigational drug are not eligible * Patients who are currently receiving other anti-cancer agents are not eligible (except leukemia patients receiving hydroxyurea, which may be continued until 24 hours prior to start of protocol therapy); patients with acute lymphoblastic leukemia may receive intrathecal therapy * Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial * Patients must be able to swallow capsules whole * Patients who have an uncontrolled infection are not eligible * Patients who have received a prior solid organ transplantation are not eligible * Patients with prior TBI, craniospinal XRT and/or those with \>= 50% radiation of the pelvis are not eligible * Patients who in the opinion of the investigator may not be able to comply with the safety monitoring requirements of the study are not eligible * Patients with known hypersensitivity to temozolomide or dacarbazine are not eligible * Phase 1 (Part A): patients who have progressed on a PARP inhibitor and temozolomide regimen are not eligible * Phase 2 (Part B): patients who have previously been exposed to a PARP inhibitor are not eligible * Phase 1 (Part A): patients with known bone marrow involvement are not eligible