This is a somewhat specific scenario. Take the normal AU where Karkat lands on earth, and gets adopted by John like a stray puppy, possibly after John nursing him back to health. John is excited to have an alien friend, and even though Karkat doesn't speak English he's sure to enjoy hanging out and watching earth movies! Brohugs and friendly pranks are abundant, and the alien doesn't seem to object.

Karkat is completely terrified. He's crash landed on a strange planet nobody even knows exists, with no way of contacting his friends. What's more, he's been taken prisoner by an alien who is far too touchy-feely, in his personal space all the time, and at one point even dropped a bucket on his head. Obviously it's only a matter of time before he's molested, because that's the only reason a troll would keep a prisoner alive this long.

On the other hand, the human is kind of weirdly attractive. Maybe being forced to pail with him wouldn't be so bad after all.
After a while, Karkat slowly develops a crush on John, while at the same time apprehensively waiting for him to make a move.
Optional: I'd would love to read that, especially if Karkat decided to get it over with and tries to make the first move with John.