This randomized phase II trial is studying topotecan to see how well it works when given with or without aflibercept in treating patients with extensive-stage small cell lung cancer. Drugs used in chemotherapy, such as topotecan, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Combinations of biological substances in aflibercept may be able to carry tumor-killing substances directly to small cell lung cancer cells. Aflibercept may also stop the growth of small cell lung cancer by blocking blood flow to the tumor. It is not yet known whether topotecan is more effective with or without aflibercept in treating patients with small cell lung cancer.