Hiding requires an opposed roll.
Can a sleeping character hide at all? If they do so, do they roll Hide when they go to sleep (for hiding their sleeping spot, etc.), or do they make an opposed roll every time someone attempts to spot them?
I'm often unable to find where my cat is sleeping, so I'd say yes, sleeping characters can still be hidden. I'd say have the character make a single hide check when they go to sleep to establish a DC (you should probably throw in a negative circumstance modifier since they won't be able to adapt to circumstances like an active, conscious hider would). Anything that wants to find them needs to beat that DC with a Spot check to find them.
I don't think I'd let people use any expendable resources to hide while asleep, and I'd probably restrict non-expendable abilities to Ex or Su abilities, although even then it's probably a case by case thing.
I don't think a sleeping character can normally hide while sleeping.
What one can do though is hide before going to sleep. Quoting from the skills section in the SRD (emphasis mine):
If you hide yourself when you go to sleep, then that's when you make the skill check. When another (N)PC searches for you, that's when (s)he will make the skill check.
So this would amount to a single hide check upon going to sleep, with multiple possible circumstance modifiers that affect the actual DC, e.g.:
For characters that don't intentionally hide before going to sleep there still may be a search check to find them if the sleeper chose an obscure location (like @JoeBedurndurn's cat). I would not include the hide skill for the character to be found though, and just set a DC similar to how you'd set a DC for finding a crate in a large warehouse or finding a specific NPC in a crowd.
For starters, I do agree with Joe's logic but quite frankly, I don't think that the hiding is the issue. I think that you can let the character in question make an INT based hide check, and let the DC reflect a concealment %. Your hide check is essentially a standing DC against any would be detector's Spot check and where Dexterity would allow them to maneuver as they detect enemy movement, Intelligence would allow them to find the best spot to stay still. Concealment rules state that you can get a miss % chance that they only really specify 20%, 50% or 100% for attacking and hitting (treating the Spotter as an attacker in this instance).
Granted, I think that a WIS based "Move Silent" check could be put into place to reflect whether or not the character snores, talks, thrashes in their sleep or whatever, but a Will save with a fairly low (12-15 would be ideal) DC should be a sufficient catch for this occurrence. I say Move Silent because a character accustomed to being quiet even in their waking hours is more likely to develop habits to do so while asleep.
But as close to RAW as I can see:
Thus their Hide check, or DC to be spotted is based off of a -5 Dexterity which for most characters stops them before they begin without cover/training.
Ex. Sneaky the Dwarven Rogue leaves his seven noisy party members to snooze somewhere less visible. He has the Stealthy feat, and 3 ranks of Hide. When he falls asleep his Hide check is effectively just the 1d20 (3+2-5), but it could be 1d20+10 for good cover. Thog the Barbarian is strolling down the road and for most of the trip Sneaky has full cover. When Thog (who arguably has a +4 spot check) is roughly 20ft away he has line of sight enough putting him at -2 penalty for distance and a -5 penalty for distraction. Pretty steep to roll a -3 Spot against +10 Hide (+0 if the cover level decreases).