While a creature is asleep (naturally, not as a result of an enchantment spell), does it continue to use its unmodified Perception score, or is it disadvantaged as a result of it being effectively in darkness/heavily-obscured/blinded?
Or phrased another way, do the environmental effects darkness or heavy obscurement, or the blinded condition, apply while a creature is sleeping?
In general, someone sleeping is considered unconscious:
While a creature sleeps, it is subjected to the unconscious condition. (XGtE)
No other conditions are mentioned in the rules so only unconscious should apply.
It is worth noting that blindness and unconscious almost completely overlap in their effects, but they are different.
One of the effects of being unconscious is:
An unconscious creature is incapacitated, can't move or speak, and is unaware of its surroundings (PHB)
So the general rule is that they are unaware of things. But, according to the rules, unconscious is the only condition applied to a sleeper.
Xanather's Guide to Everything has some guidance this. On the section talking about mechanical effects of sleeping it says:
Whispers don’t disturb sleep, unless a sleeper’s passive Wisdom (Perception) score is 20 or higher and the whispers are within 10 feet of the sleeper. Speech at a normal volume awakens a sleeper if the environment is otherwise silent (no wind, birdsong, crickets, street sounds, or the like) and the sleeper has a passive Wisdom (Perception) score of 15 or higher. (XGtE)
Which implies that a sleeper does indeed use an unmodified passive perception at least for audible effects.
But I think some common sense rulings can be applied. A normal sleeping person with their eyes closed obviously can not see most things (unless maybe a bright light). So a robber who is, say, in the area of effect of a silence spell would have no chance of being seen by the sleeper assuming no other phenomena wake them up.
But it gets more complicated when you ask what kind of check would be needed, if any, for a sleeper to notice and possibly to wake up to a lantern or bright light shining on them. In this case I would also tend to use passive perception (possibly at disadvantage: passive perception - 5), but this is a case not really defined at all in the rules.
Thus, a DM should use the above guidance and determine how best to apply the rules we do have to any given situation that might call for this kind of ruling.
These answers are correct, but they do not address what I see as the key issue. While asleep, you are unconscious and do not perceive your surroundings, BUT what determines whether you wake?
There is no standard rule that I know of to apply, so I look at 2 things: rolls are for uncertainty, and the DM decides (though for a DM looking for answers this response is NEVER helpful). So first, you as DM decide whether there is a chance to wake up. I would base this on typical behavior plus specific events. Do they all crash after a party, or are some always light sleepers, etc?
In any case, Advantage and disadvantage always apply. There are 2 barriers. The sleeper is probably at a disadvantage both to wake and to notice anything. I generally rule that an elf who is meditating is -5PP. In this case, I would also apply a second level of disadvantage, as -10 to PP or dis each to PP and Stealth.
To run it even simpler, you could say only a 1 wakes a creature, and then you get a chance to hide because you KNOW that you just made a loud noise.
