 This randomized phase II trial studies the effects of acetylcysteine and topotecan hydrochloride on the tumor microenvironment, or cells that make up a tumor, compared to topotecan hydrochloride alone in patients with ovarian, fallopian tube, or primary peritoneal cancer that has not responded to treatment persistent or has returned after a period of improvement recurrent and is high grade likely to grow and spread quickly. Research has shown that cancer cells may be able to convert nearby normal cells into cancer cells. Acetylcysteine may stop this from happening. Topotecan hydrochloride is a chemotherapy drug used to treat ovarian cancer, and may help acetylcysteine work better. This trial studies the effect of acetylcysteine and topotecan hydrochloride on the tumor microenvironment to see if they can help make it more difficult for tumor cells to grow. 