Exsurgent: The devs don't post here - you might want to ask that question on the Steam forum to get a clear answer, they are very active over there.

I THINK I remember the Steam demo having a save system or something like that. Anyways, the game has been changed quite a bit since the original pitch. It's no longer a procedurally-generated roguelike, for example, so I suspect permadeath probably isn't a thing with this game anymore, either.

EDIT: From the Rock Paper Shotgun review:
"Death is a hard reset and obliterates your progress entirely, returning you to whichever checkpoint you last happened to touch, rolling back any experience points you gained, any equipment changes you made and items you picked up."
https://www.rockpapershotgun.com/undungeon-review