Okay, I don't remember a lot, but here's what I got.

 Dean and Sam end up staying with a couple somewhere or another that are actually possessed by their past lives due to a magical amulet. I think they were soulmates too. Dean and Sam are supposed to receive the amulet next (which they end up doing) and they live together for their specified amount of time as their past lives. I remember that the previous couple that were possessed didn't stay together after their possession ended because the woman was a lesbian. I think I remember Dean freaking out after they are de-possessed and he takes off for a while. Eventually they are able to track down the witch that was giving the amulet to people and letting their past lives take over their bodies.

That's about all I remember, but I really loved this story and want to reread it, but I cannot find it anywhere. TIA!

The story is A Place to Rest My Spirit by Miss 'Drea and the link is located here. Thank you Katsheswims!