Cancer stem cells (CSCs) may be responsible for tumour dormancy, relapse and the eventual death of most cancer patients. In addition, these cells are usually resistant to cytotoxic conditions. However, very little is known about the biology behind this resistance to therapeutics. Here we investigated stem-cell death in the digestive system of adult Drosophila melanogaster. We found that knockdown of the coat protein complex I (COPI)-Arf79F (also known as Arf1) complex selectively killed normal and transformed stem cells through necrosis, by attenuating the lipolysis pathway, but spared differentiated cells. The dying stem cells were engulfed by neighbouring differentiated cells through a draper-myoblast city-Rac1-basket (also known as JNK)-dependent autophagy pathway. Furthermore, Arf1 inhibitors reduced CSCs in human cancer cell lines. Thus, normal or cancer stem cells may rely primarily on lipid reserves for energy, in such a way that blocking lipolysis starves them to death. This finding may lead to new therapies that could help to eliminate CSCs in human cancers.