A crashing program obviously has undefined behavior, which means it could do anything, including very harmful things. A quite typical outcome would be corrupting its own data. As a responsible operator of services, you'll have a good backup strategy of course, so the impact of such behavior would be limited, but still you should be aware that just restarting something that crashed before you know why and how it crashed is quite risky. You should weigh that risk against the (business?) risk of the particular service being down for a while...

CC: @joel@piou.foolbazar.eu @stefano@bsd.cafe