Situationally dependent, as others have said.
If the PCs have access to revival effects in the field, no problem. Carry on. It's then on the remaining players/PCs as to how long it'll be before good ol' Deadly Dooright is upright again.
But if they don't:
If there's a reasonable means of introducing or having the party find a new PC in what the DM knows (or guesses) might be coming next in the adventure, get the dead PC's player started on rolling up a new PC ASAP. Lob an extra prisoner into the castle dungeon, for example, or modify one already there, and let the PCs run on to it. Or have the new PC be found blundering around in the woods with no idea how it got there. Etc. (note that if you place the new PC in a static location there's a slight but non-zero risk the other PCs never find it, or take ages to do so; I was once in this situation and it took the party five sessions to find me!)
If the party can relatively easily return to town, simply pointing out that now Deadly is gone the party is missing or short on whatever class/abilities he had should be enough to turn 'em around. Once back in town either revival or meeting a new PC should be easy.
If, as in the example, the party have passed a point of no return then options become fewer; and down to near zero if where they've gone is a place where nothing alive normally goes. Here Deadly's player might just have to wait it out, or you-as-DM could have the party stumble over the new PC and say it somehow wound up here by accident.