Cancer stem cells likely survive chemotherapy or radiotherapy by acquiring mutations that inactivate the endogenous apoptotic machinery or by cycling slowly. Thus, knowledge about the mechanisms linking the activation of an alternative cell death modality and the cell cycle machinery could have a transformative impact on the development of new cancer therapies, but the mechanisms remain completely unknown. We investigated the regulation of alternative cell death in Drosophila larval brain neural stem cells (neuroblasts) in which apoptosis is normally repressed. From a screen, we identified two novel loss-of-function alleles of the Cdc20/fizzy (fzy) gene that lead to premature brain neuroblast loss without perturbing cell proliferation in other diploid cell types. Fzy is an evolutionarily conserved regulator of anaphase promoting complex/cyclosome (APC/C). Neuroblasts carrying the novel fzy allele or exhibiting reduced APC/C function display hallmarks of necrosis. By contrast, neuroblasts overexpressing the non-degradable form of canonical APC/C substrates required for cell cycle progression undergo mitotic catastrophe. These data strongly suggest that Fzy can elicit a novel pro-survival function of APC/C by suppressing necrosis. Neuroblasts experiencing catastrophic cellular stress, or overexpressing p53, lose Fzy expression and undergo necrosis. Co-expression of fzy suppresses the death of these neuroblasts. Consequently, attenuation of the Fzy-dependent survival mechanism functions downstream of catastrophic cellular stress and p53 to eliminate neuroblasts by necrosis. Strategies that target the Fzy-dependent survival mechanism might lead to the discovery of new treatments or complement the pre-existing therapies to eliminate apoptosis-resistant cancer stem cells by necrosis.