JI'm typing this without reading the other replies.
My wife's step-dad routinely buys wrecks from his brother. They often to go the auctions, buy a car, and his brother fixes them. Family members typically pay him for the repairs then drive the vehicle for a year or more. A couple cars in the family have were bought 3-4+ yrs ago and are doing well.
From talking to both of them, it really depends on the car and the damage. They have bought cars that had minor "appearance" damage, but they've also bought cars with frame damage. Typically when they are done, you can't tell it was in a wreck, no matter how bad it was. $$$ wise it works out very much to their favor to do it this way. If they do end up selling to another party, they always tell them exactly what the damage was, and what they did to repair. Also, in PA, the title becomes an "R" title, which I think stands for "repair". Similar to a Salvage title in other states I think.
One thing to note, I think most, if not all the time, they are dealing with a car that does not have major engine problems. ALthough I know they did have a couple of roll overs, as well as a flood car or two. 99% of the time, it's body work--they had a Monte Carlo that needed pretty much every body panel, and all glass replaced. But they bought it for like $2k. It's still in the family after 6 yrs/100K+ miles.