 This phase I trial studies the side effects and best dose of veliparib when given together with capecitabine and temozolomide in treating patients with neuroendocrine tumor that has spread to other places in the body and usually cannot be cured or controlled with treatment, has returned after a period of improvement, and cannot be removed by surgery. Veliparib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as capecitabine and temozolomide, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. 