Sitting in the Raid a bit ago, we had some playing the "let's sit here and not roll, so people will leave and we get the loot without having to roll" game.
Seems to me that we need a roll timer. That goes into effect when the dungeon or raid is over and the final chest is opened.
So after the final boss is defeated, the chest is opened. You've got 60 seconds, maybe 90 seconds, to make your roll decisions. When the timer runs out, anything you have not rolled on is automatically passed on.
This will prevent people from camping out and refusing to roll. Take into account the "death" animation if you want. But any big cutscenes shouldn't trigger until after you try to leave the dungeon or raid anyways.