Normally, it's not an issue. Every state varies but it typically has to be inspected by a police department or state trooper to make sure it is roadworthy. Not a big deal, do it all the time in Missouri, Kansas and Arkansas. Then you apply for a "rebuilt" title and they give you tags and you're on your way. Some insurance companies won't allow full coverage on a rebuilt car but a lot dont care either. Kind of depends on how much the car is worth and how much they think they can get out.of you.
If the title still says "salvage", and they've fixed it, I'd beat them up on price. Because you have to show receipts for every major part put on the car. Coming up with legit receipts could be a challenge.
If the title says "rebuilt", then you shouldn't need receipts. I would call your local DMV and verify the process because each state is different.
Almost all I drive is "salvage/rebuilt" cars. Look, run & drive great and no full coverage insurance because I can pay cash and be done with them. Just because the title says "salvage/rebuilt" does not mean it was set on fire and pushed off a cliff as CARFAX would have you believe. It can be something very minor, out of gas, really, to rolled into a ball. Bought 3 in a row that were salvage and out of gas because they wouldnt start. They assume engine damage and list them as stationary. When in fact the customer drained the gas tank or the yard employees drained the tank and put the gas in their car.