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

Known standard therapy for the patient's disease that is potentially curative or definitely capable of extending life expectancy

Prior treatment with a PARP inhibitor or topotecan

Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements

Any of the following prior therapies:

* Chemotherapy =\< 4 weeks prior to registration

* Mitomycin C/nitrosoureas =\< 6 weeks prior to registration

* Immunotherapy =\< 4 weeks prior to registration

* Biologic therapy =\< 4 weeks prior to registration

* Radiation therapy =\< 4 weeks prior to registration

* Radiation to \> 25% of bone marrow

* Investigational therapy or any ancillary therapy considered investigational (utilized for a non-Food and Drug Administration \[FDA\]-approved indication and in the context of a research investigation) =\< 4 weeks prior to registration; subjects with prostate cancer will be permitted to continue hormone therapy

Failure to fully recover from acute, reversible effects of prior chemotherapy regardless of interval since last treatment

New York Heart Association classification III or IV

Known central nervous system (CNS) metastases or seizure disorder; patients with known brain metastases that have been successfully treated and stable for \>= 6 months without requirement for corticosteroids and without seizure activity will be eligible

Any of the following:

* Pregnant women

* Nursing women

* Men or women of childbearing potential who are unwilling to employ adequate contraception

Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens

Immunocompromised patients (other than that related to the use of corticosteroids) including patients known to be human immunodeficiency virus (HIV) positive

Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm

Other active malignancy, except non-melanotic skin cancer or carcinoma-in-situ of the cervix

* Note: If there is a history of prior malignancy, they must not be receiving other specific treatment (other than hormonal therapy) for their cancer

History of myocardial infarction =\< 6 months, or congestive heart failure requiring use of ongoing maintenance therapy for life-threatening ventricular arrhythmias

More than 2 prior chemotherapy regimens for the current malignancy; full dose chemotherapy used in conjunction with concurrent radiation therapy will be included as prior therapy

* Note: Prior hormonal therapy (e.g. leuprolide, aromatase inhibitors, tamoxifen) and immunotherapy will be allowed and not included as a prior chemotherapy; if the chemotherapy regimen is altered during the course due to issues with tolerability or safety, the regimen will be counted as one; using the same regimen at recurrence is counted as one regimen; the addition of bevacizumab to a prior regimen is considered one regimen

What this study is about