This phase I trial studies the side effects and best dose of ATR kinase inhibitor VX-970 and irinotecan hydrochloride in treating patients with solid tumors that have spread to other places in the body and usually cannot be cured or controlled with treatment (advanced) or cannot be removed by surgery. ATR kinase inhibitor VX-970 and irinotecan hydrochloride may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth.