At our school
theatre we have a separate
props commitee that is in charge of the smaller items. The actors are told that if they don't grab a prop, then don't count on it getting out there. On some occaisions, an actor won't be able to get off stage, changed, grab the prop, and get back on stage in time. If they ask me nicely and aren't ignorant or cocky, I usually do what I can to help them out. In some cases, an important prop won't get on stage so I make sure that it gets out there (usually I have an actor take it on because they are all taught how to improv. if need be). Even though they can improv. , it looks silly when they don't have a major prop (like one that is actually talked about in the dialogue).
-Nate