I was playing solo, just killed Shadowheart because of her attitude towards Githyanki, and accidentally ran through some fire an died (An ignoble end for my Wizard).
I made all three death saves but then couldn't do anything as I was still downed.
If that's the way you want to go fine, although I'd rather you regained consciousness at 1 hp, but you need to tell the player that the game is over and they have to reload.
I spent 5 minutes trying to figure out what to do next to get my character going.
If the entire party is down, even if that party is 1, you should get a reload screen IMHO.