Extinction events impact the trajectory of biological evolution significantly. They are often viewed as upheavals to the evolutionary process. In contrast, this paper supports the hypothesis that although they are unpredictably destructive, extinction events may in the long term accelerate evolution by increasing evolvability. In particular, if extinction events extinguish indiscriminately many ways of life, indirectly they may select for the ability to expand rapidly through vacated niches. Lineages with such an ability are more likely to persist through multiple extinctions. Lending computational support for this hypothesis, this paper shows how increased evolvability will result from simulated extinction events in two computational models of evolved behavior. The conclusion is that although they are destructive in the short term, extinction events may make evolution more prolific in the long term.