Sleepers are unaware of their surroundings in general
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.
Audible things, at least, use unmodified passive perception
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.
Any other effects would be outside the explicit rules so would be the DM's decision
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.