Diseased animals do not die peacefully on their deathbeds. In nature, a significant part of disease-related mortality comes from the increased risk of predation that hosts carrying virulent infections are exposed to. Moreover, since pathogens evolve quickly, the evolutionary dynamics of a pathogen can interact with the population dynamics of a predator. The resulting eco-evolutionary system may exhibit rich dynamics with multiple attractors and limit cycles. We use a novel technique to provide a constructive proof that the system can exhibit stable limit cycles under realistic assumptions about the model ingredients, and we also perform a detailed bifurcation analysis of a fully specified predator-prey-pathogen system.