The efficient removal of dead cells is an important process in animal development and homeostasis. Cell corpses are often engulfed by professional phagocytes such as macrophages. However, in some tissues with limited accessibility to circulating cells, engulfment is carried out by neighboring non-professional phagocytes such as epithelial cells. Here, we investigate the mechanism of corpse clearance in the Drosophila melanogaster ovary, a tissue that is closed to circulating cells. In degenerating egg chambers, dying germline cells are engulfed by the surrounding somatic follicular epithelium by unknown mechanisms. We show that the JNK pathway is activated and required in engulfing follicle cells. We find that the receptor Draper is also required in engulfing follicle cells, and activates the JNK pathway. Overexpression of Draper or the JNK pathway in follicle cells is sufficient to induce death of the underlying germline, suggesting that there is coordination between the germline and follicular epithelium to promote germline cell death. Furthermore, activation of JNK bypasses the need for Draper in engulfment. The induction of JNK and Draper in follicle cells occurs independently of caspase activity in the germline, indicating that at least two pathways are necessary to coordinate germline cell death with engulfment by the somatic epithelium.