Veliparib and Topotecan Hydrochloride in Treating Patients With Solid Tumors, Relapsed or Refractory Ovarian Cancer, or Primary Peritoneal Cancer

Inclusion Criteria: * PHASE I: Adult patients with histologically confirmed solid tumor malignancy that is metastatic or unresectable and for which standard curative measures or other therapy definitely capable of extending life expectancy does not exist * PHASE II: All patients enrolled in the Phase II portion of this trial must have a history of biopsy-proven ovarian, fallopian tube or primary peritoneal cancer * Patients must have received \< 3 lines of prior therapy and have relapsed less than a year from their last platinum regimen; regimens that are used twice (for example carboplatin and paclitaxel) can be counted as one; if a regimen is changed during the course of treatment due to side effect profile or allergy, the course of therapy is counted as one regimen; (for example, if docetaxel is substituted for paclitaxel due to a reaction during the initial course of adjuvant therapy, this is considered one regimen) * Patients must have measurable disease with at least one lesion whose longest diameter can be accurately measured as \>= 2.0 cm with conventional techniques or as \>= 1.0 cm with spiral computed topography (CT); if spiral CT is used, it must be used for both pre- and post- treatment tumor assessments * Absolute neutrophil count \>= 1500/mcL * Hemoglobin \>= 9.0 g/dL * Platelets \>= 100,000/mcL * Total bilirubin =\< 1.5 x the upper limit of normal (ULN) * Serum glutamic pyruvic transaminase (SGPT) (alanine aminotransferase \[ALT\]) or serum glutamic oxaloacet…