While employers are technically responsible, there is also a mentality from long long ago that is along the lines of, "If you can walk, get onstage." I've heard stories of ballerinas with broken ankles completing ballets. More recently, I think Rachelle Rak fell through a trap door, finished the show, and then got her broken ribs taken care of. I don't know if it's just been passed down from pre-union days or what, but that mentality is very very strong among performers.
Some people paint, some people sew, I meddle.