Veliparib and Floxuridine in Treating Patients With Metastatic Epithelial Ovarian, Primary Peritoneal Cavity, or Fallopian Tube Cancer

Inclusion Criteria: * Histologically confirmed epithelial ovarian, primary peritoneal or fallopian tube malignancy that is metastatic and for which standard curative measures do not exist * Disease confined to the intraperitoneal and retroperitoneal cavity; Note: nodal disease below the diaphragm, implants adherent to the surface of the liver or intrahepatic lesions will not be exclusionary; patients remain eligible if all intrahepatic tumor is debulked or ablated by the time treatment is initiated * EXPANSION PHASE ONLY: Evaluable or measurable disease with the largest nodule measuring less than 5 cm in greatest dimension by radiographic imaging after debulking procedure * Candidate for and willingness to have a surgically placed intraperitoneal catheter and tissue acquisition at the time of port placement; note: if an intraperitoneal catheter is already in place, a tumor biopsy will still be required; a guided core-needle biopsy is sufficient in these cases * Able to swallow and absorb the medication * Obtained =\< 7 days prior to registration: Absolute neutrophil count (ANC) \>= 1500/mm\^3 * Obtained =\< 7 days prior to registration: Platelets (PLT) \>= 100,000/mm\^3 * Obtained =\< 7 days prior to registration: Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) * Obtained =\< 7 days prior to registration: Creatinine =\< 1.5 x institutional ULN * Obtained =\< 7 days prior to registration: Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) =\< 3 x institutional ULN * Obtained =\< 7 days prior to registration: Hemoglobin (Hgb) \> 9.0 mg/dl * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, or 2 * Ability to provide informed written consent * Life expectancy \>= 12 weeks * Women of childbearing potential only: negative pregnancy test done =\< 7 days prior to registration Exclusion Criteria: * Known standard therapy for the patient's disease that is potentially curative or definitely capable of extending life expectancy; note: patients with recurrent platinum-sensitive ovarian, primary peritoneal or fallopian tube will be allowed, if the investigator believes the study treatment is a better alternative to initiation platinum-based chemotherapy, such as patients with a prior platinum allergy or low volume disease for whom platinum-based therapy is deferred until a later date * More than 4 prior chemotherapy regimens; note: repeat use of regimens count as 1 prior regimen; switching front-line therapy regimens (for example, from intraperitoneal to intravenous therapy) for reasons other than progression will count as 1 prior therapy; bevacizumab and other 'targeted' agents will count in the total number of prior regimens; vaccine therapies will not count in the total of prior therapies * 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 =\< 28 days prior to registration * Mitomycin C/nitrosoureas =\< 42 days prior to registration * Immunotherapy =\< 28 days prior to registration * Biologic therapy =\< 28 days prior to registration * Radiation therapy =\< 28 days prior to registration * 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) =\< 28 days prior to registration * Prior poly (adenosine diphosphate \[ADP\]-ribose) polymerase (PARP) inhibitor therapy * Failure to fully recover from acute, reversible effects of prior chemotherapy regardless of interval since last treatment * Significant cardiovascular disease defined as congestive heart failure (New York Heart Association class III or IV cardiac disease), angina pectoris requiring nitrate therapy or recent myocardial infarction (=\< 6 months prior to registration) * Metastatic disease outside the intraperitoneal cavity and retroperitoneum, intrahepatic lesions, or pleural effusions; significant ascites precluding catheter placement; exception: intrahepatic lesions removed or planning to be removed during the debulking procedure * Any of the following: * Nursing women * Pregnant women * Women of childbearing potential who are unwilling to employ adequate contraception (non-barrier method) * Immunocompromised patients (other than that related to the use of corticosteroids) with the exception of patients known to be human immunodeficiency virus (HIV) positive and have a cluster of differentiation 4 (CD4) count \> 400 and do not require antiretroviral therapy * Receiving any other investigational agent that would be considered a treatment for the primary neoplasm * Other active malignancy =\< 1 year prior to registration * EXCEPTIONS: Non-melanotic skin cancer or carcinoma-in-situ of the cervix * NOTE: If there is a history or prior malignancy, they must not be receiving other specific treatment for their cancer