Prey resurgence, in which a mortality event paradoxically leads to an increase in a prey population, has been documented many times, particularly when the prey is a pest and the event is a human action intended to reduce its numbers. Here we have explored a mechanism for prey resurgence with the following properties. First, the prey has a single predator. Second, the predator is subject to a strong Allee effect and therefore has a minimum viable population level. Third, a mortality event reduces the predator population beneath its minimum viable level, so that the predator dies out. Fourth, the prey resurges as its predator dies out. We have applied this mechanism to a general predator-prey model, deriving conditions for prey resurgence by any factor R>1. Then we have shown, for a specific model, that these conditions can hold. Simulations corroborate our analysis. Finally, we place our results in a modern context by recognising that potential causes for prey resurgence are currently widespread.