Veliparib, Capecitabine, and Temozolomide in Patients With Advanced, Metastatic, and Recurrent Neuroendocrine Tumor

Inclusion Criteria: * Pathologically confirmed metastatic unresectable well differentiated (low grade and intermediate grade) neuroendocrine tumors (Ki-67 \< 20% and mitotic rate \< 2 per 10 high power field) that demonstrate progressive disease (by serial computed tomography \[CT\] or magnetic resonance imaging \[MRI\] scans) in past 12 months including * Carcinoid tumors originating anywhere in the body including the gastrointestinal (GI) tract or bronchial tree or thymus * Pancreatic neuroendocrine tumors (including functional and non-functional islet cell, insulinomas and glucagonomas) * Pheochromocytomas * Gastrinomas (Zollinger-Ellison syndrome) * Multiple endocrine neoplasia (MEN type I/II), * Adrenal carcinomas with NET markers by immunohistochemistry (IHC) or serum * Somatostatinoma * VIPoma (vasoactive intestinal peptide) * Merkel cell tumors * Medullary thyroid carcinoma * Neuroendocrine tumors of unknown primary site * Patients must have progressed on octreotide therapy and/or radioactive isotopes linked to octreotide or its congeners if they had a positive octreotide scan; patients who have negative or mildly positive octreotide scans are exempt from this requirement * Somatostatin analogs can be continued at their tolerated dose in patients with functional symptoms related to underlying disease such as in functional islet cell, insulinomas, glucagonomas etc * Patients may have received prior chemotherapy for advanced disease including either capecitabine or temozolomide single agent as long as it did not include combination of capecitabine and temozolomide * Patients must have completed prior (non-excluded) anti-cancer therapy (including surgery or chemotherapy or hepatic embolization/chemoembolization or radioactive isotopes i.e. yttrium 90) at least 4 weeks prior to day 1 * Patients with no brain metastases or a history of previously treated brain metastases who have been treated by surgery or stereotactic radiosurgery at least 4 weeks prior to enrollment and have a baseline MRI that shows no evidence of active intracranial disease and have not had treatment with steroids within 1 week of study enrollment * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * Anticipated life expectancy of greater than 3 months * Patients must have measurable disease either primary and/or metastatic masses reproducibly measurable in one or two diameters by Response Evaluation Criteria in Solid Tumors (RECIST) criteria 1.1 parameters by CT scan or MRI scan; positron emission tomography (PET) or octreotide scans are useful adjuncts but will not be used to measure response * Granulocytes \> 1,500/ml * Platelets \> 100,000/ml * Hemoglobin \>= 10 g/dl * Creatinine \< 1.5 x upper limit of normal (ULN) or creatinine clearance \>= 50 mL/min/1.73 m\^2 for subjects with creatinine levels above institutional normal * Bilirubin \< 1.5 x ULN * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \< 3 x ULN (\< 5 x ULN if liver metastases are present) * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately; men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of veliparib, capecitabine and temozolomide administration * Ability to understand and the willingness to sign a written informed consent document * Patients must be able to swallow pills Exclusion Criteria: * Prior chemotherapy with combination of capecitabine (or 5-flourouracil \[5-FU\]) "and" temozolomide (or dacarbazine \[DTIC\]) will be excluded; patients can have had prior therapies up to 3 prior chemotherapy regimens such as streptozocin, anthracyclines, irinotecan, etoposide, or a platinum agent including single agent capecitabine (or 5FU) or temozolomide (or DTIC). * History of severe hypersensitivity reaction to capecitabine, 5-FU, temozolomide or DTIC will be excluded (i.e. anaphylaxis or anaphylactoid reactions) * Patients who have active or uncontrolled infection or serious medical or psychiatric illness preventing informed consent or on intensive treatment * Patients with brain metastases are excluded * Patients with uncontrolled seizures or any neurological conditions resulting in increased risk for seizures are not eligible for study entry * Patients with documented central nervous system (CNS) ischemia and/or infarction, whether symptomatic or discovered incidentally without clinical symptoms, will be excluded from study participation * Patients with a history of the arterial or venous thromboembolism within =\< 12 months of study entry are not eligible * Human immunodeficiency virus (HIV)-positive patients on antiretroviral therapy are excluded from the study * Patients with another active malignancy within the past five years except for carcinoma in situ of cervix or in situ carcinoma of the bladder or non-melanomatous carcinoma of the skin * Clinically significant and uncontrolled major medical conditions including but not limited to: active uncontrolled infection, psychiatric illness/ social situation that would limit compliance with study requirements; any medical condition, which in the opinion of the study investigator places the subject at an unacceptably high risk for toxicities * Patients who are receiving any other investigational agents * Major surgical procedure within 4 weeks of treatment * Patients may not have any clinically significant cardiovascular disease including the following: * Myocardial infarction or ventricular tachyarrhythmia within 6 months * Prolonged QTc \> 480 msec at baseline * Symptomatic congestive heart failure (CHF) of New York Heart Association (NYHA) functional class \>= 3 * Major conduction abnormality (unless a cardiac pacemaker is present) * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with capecitabine or temozolomide or veliparib