Happens all the time. Some wil wask and store, some just pitch on the old cake. Some things to consider:
1. Always pitch to a darker recipie of a recipie of the same color. Pithching to a lighter wort will likely impart flavors you did not intend.
2. Having a cake hanging around for a prolonged period of time will increase the likelyhood that bacteria will infect the cake. Personally I would wash and store the cake unless I was planning to use it within 24 hours.
3. If you ae interested in yeast propogation, consider harvesting, either from a spent cake or (as I do) from a split starter.