I think it would be a good idea if forced-turn-based mode is engaged around a character making death saves. I lost a guy a couple days ago because a cutscene started, and someone was making death saves, and failed.
I think it would also be neat if death saves were rolled manually, but there'd probably need to be some sort of automatic timer, to prevent people from staying in death saves mode indefinitely from across the map while a party member comes to catch up.