I've depped for a good few function bands over the years and 80% of the material is familiar and, as a rule, the drummer broadcasts the endings and changes clearly enough to make up for any idiosyncrasies that may have crept in. I'm happy enough to learn the songs that I don't know because this is my hobby and I do it for the enjoyment rather than the pay but also, I'm bound to be asked to play those songs again in the future so there is an element of investment of time, too.
Having said that, I take Bilbo's point up to a point and people should also be cautious about getting a dep who is outwith their usual milieu. I say this next bit and then run for my flame-retardant overalls, there are some jazz bassists who have a slightly condescending approach to non-jazz music and have the (mistaken) attitude that because they can play jazz, they can play anything. That can grate.