The story is in short: occassionally Sin gets haunted by things he kills
The long story with Lydia. Lydia is Tetsurou's sister. Sin and her went out to the mall together. He accidentally hurt her (i forget exactly. There was something about a garbage can I think), tried to help her because it's Tetsurou's sister, but ended up killing her by accident instead. She became a ghost, but Tetsurou doesn't brain strong enough to tell the difference. SO they're living like normal, while Sin occassionally gets a voiyeristic ghost peeping in on him.