My very first job before getting into radio was a grounds keeper at a local "Memorial Park", as we liked to call it.  I have first hand knowlege on this subject.  Our grave yard was situated on a hillside.  This sometimes meant that we had to actually dig the graves by hand instead of using a backhoe.  Anyway, I hate to say that sometimes the casket does not make a gracefull landing in the vault.  One time we were burrying this man, and his casket was oversized, and his family only ordered a normal size vault(the vault is the cement box that the casket is put into) After the fmily left, we had to take the handles off of the casket to make it fit.  It was a tight fit, but we finally got him in.  One time (i was not working there for this one) A groundskeeper was lowering a casket, he did not wait until the family left the cemetary, and seeing as how the grave was in a hilly area as he lowered the casket, he had to use his foot to guide the casket down.  The family totally flipped out, they thought this guy was jumping up and down on their relitive.  So to answer your question, they usually wait for the family to leave...because accidents can happen.