Stability selection is the process by which species are lost from a community due to a structural susceptibility to extinction. Stability selection is non‐adaptive because it does not lead to the evolution of traits that increase individual fitness. However, stability selection could still drive evolutionary change because the stability of populations is linked to heritable traits. Here we demonstrate both phenomena with a live predator–prey system. We show that the stability properties of a predator–prey pair vary with prey genetics, indicating the potential for differential extinction to influence the genotypic makeup of populations. Second, we show that the loss of unstable predator–prey pairs in subpopulations from the overall population can lead to trait evolution in the aggregate population, providing empirical support for the stability selection mechanism. Our results indicate that community‐level processes such as predator–prey interactions can generate eco‐evolutionary change at the population scale.