If a party stays overnight in the dungeon or the wilderness, do they heal at all? The rules say a person with a full day's rest in reasonable conditions heals 1d3 HP. But what if they just get an uninterrupted night's sleep in a dungeon setting? Saying that it's worth 0 HP seems to make delves away from "home base" functionally impossible without magical healing or 2 levels of Healing proficiency.
Until I hear something official, I have temporarily house-ruled it that they get 1 HP back for an uninterrupted night's sleep.
If they actually managed to rest for 8 hours in a dungeon, I'd let them heal 1d3 HP, but most dungeons still have random encounters so they'd have to have found a secret room to post up in or somehow barred a door.
The rules make references in the healing proficiency to added benefits for complete rest, which I think is in contrast to your standard 8 hours of rest.
I would say yes, a full day "in reasonably sanitary conditions" is the prerequisite for 1d3. Normally I'd give 0 for anything less, but in the right campaign 1 hp for uninterrupted sleep seems fine.