The development of oncogene targeted therapies over the past few decades facilitated by cancer driver gene identification through next generation sequencing has resulted in impressive clinical responses against late-stage cancers. However, robust responses are hindered by acquired drug resistance. This is the scenario where a tumor initially responds to therapy, but then regrows even in the presence of continued drug treatment. Here, we investigate cancer persister cells as a model of acquired drug resistance to identify processes that allow tumors to overcome drug pressure. Single cell transcriptomic profiling revealed well-characterized drug resistance processes occurring in persister cells such as epithelial-mesenchymal transition. Interestingly, it also revealed apoptotic signaling as a process shared across multiple persister cell models. We found that cancer persister cells survive caspase 3 activation and minority mitochondrial outermembrane permeabilization (MOMP). This sublethal apoptotic signaling activates the nuclease DFFB. DFFB causes mutagenic DNA damage resulting in persister regrowth through both genetic and nongenetic mechanisms. Inhibition of DFFB blocked persister cell regrowth both in cell culture and in vivo. Given the need for targets against stress adaptation mechanisms, DFFB represents a promising therapeutic target that could extend the efficacy of already available anti-cancer therapies.