Sudden catastrophic events like fires, hurricanes, tsunamis, landslides and deforestation increase population densities in habitat fragments, as fleeing animals encroach into these refuges. Such sudden overcrowding will trigger transient fluctuations in population size in the refuges, which may expose refuge populations to an increased risk of extinction. Until recently, detailed information about the operation of density dependence in stage-structured populations, and tools for quantifying the effects of transient dynamics, have not been available, so that exploring the extinction risk of such transient fluctuations has been intractable. Here, we use such recently developed tools to show that extinction triggered by overcrowding can threaten populations in refuges. Apart from situations where density dependence acts on survival, our results indicate that short-lived species may be more at risk than longer-lived species. Because dynamics in local populations may be critical for the preservation of metapopulations and rare species, we argue that this aspect warrants further attention from conservation biologists.