Throughout their lifetime, cells may suffer insults that reduce their fitness and disrupt their function, and it is unclear how these potentially harmful cells are managed in adult tissues. We address this question using the adult Drosophila posterior midgut as a model of homeostatic tissue and ribosomal Minute mutations to reduce fitness in groups of cells. We take a quantitative approach combining lineage tracing and biophysical modeling and address how cell competition affects stem cell and tissue population dynamics. We show that healthy cells induce clonal extinction in weak tissues, targeting both stem and differentiated cells for elimination. We also find that competition induces stem cell proliferation and self-renewal in healthy tissue, promoting selective advantage and tissue colonization. Finally, we show that winner cell proliferation is fueled by the JAK-STAT ligand Unpaired-3, produced by Minute(-/+) cells in response to chronic JNK stress signaling.