Inspired pretty entirely by a tumblr post that said when Jensen asked why Dean didn't have a beard in Purgatory, the writers replied, "Dean has knives."
Overture
Dean lets his beard grow out the first week. Turns out that Purgatory Drugstore (on the corner of That Tree Over There and More Endless Fucking Trees Everywhere) is running low on shaving cream and the only razors they have in stock are the claws attached to the end of a monster's fingers, and that's not the kind of close shave he's looking for. Plus he's got more important things to worry about than having a smooth chin, such as staying alive and finding a wayward Angel.
And he's sure Sam will get him out of here before it's an issue, anyway.
But the days pass and a week turns into two and his beard is really starting to itch and then it doesn't anymore but it's still hot, warm and sweaty and uncomfortable in the perpetually humid air of Purgatory and Dean finally takes a knife to his face. He only has the one silver blade he'd had stashed in his jacket at the start of this mess and the steel switchblade he always carries in his back pocket, until he kills a rugaru and loots the poorly-made axe of bone and wood it'd tried to take his head off with. But that would just as soon take his head off if he tried to shave with it, too, so he picks a place by a stream with a thick tree at his back and goes to work with his silver knife, only having to stop once to kill a werewolf that thought it could sneak up on him while his guard was down.
His guard's never down here.
Dean doesn't know why his beard is growing, anyway. The rest of his hair doesn't seem to be, though maybe it's just too early to tell. Clearly the rules of Purgatory are different than earth's, since he gets tired but doesn't need to sleep, pisses but doesn't shit, gets thirsty but not hungry. And a good thing, too, since the only thing he's found to eat around here are the corpses of the monsters he kills. He's not quite that desperate to satisfy his oral fixation, thanks. Despite his lack of appetite, he's still surprised at how much he misses eating, something he's done (nearly) every day of his life. He thinks about stripping a chunk of bark off a tree, just to have something to chew on, but he has no idea how putting anything from Monsterland in his mouth might affect him.
He's sure Sam will get him out of here before it gets too bad, anyway.
He kind of wonders what's taking the kid so long and resolutely doesn't think about forty years without rescue. But (not) thinking about Hell makes him remember what Crowley said about Purgatory so long ago (location, location, location). Hell-adjacent. It stands to reason, then, that maybe time flows differently here than on earth, slower, like in Hell. (Not that he's thinking about that.) Maybe only five minutes have passed topside. Maybe Sam is still standing dumbstruck in the middle of SucroCorp, wondering where his big brother and Cas disappeared to. Maybe he hasn't even had a chance to bust out the lore and start researching yet.
Dean doesn't know if this thought is better or worse. Sometimes he swears he can hear distant whistling off through the trees. He thinks he might be going a little bit insane.
He's sure Sam will get him out of here before it's a real problem.