in many states you cannot carry full coverage on a salvage vehicle, collision only, no comprehensive...(full coverage has nothing to do with warranty, has to do with vehicle reliability based on the insurance safety board)...also very few finance companies will approve a loan on a salvage vehicle, nationwide.
however you can take out a personal loan and use that money for the vehicle as neither party will have issue with that...if you can get a personal loan that is, which you said your parent would be getting, so no prob really...
in a handful of states you can repair the car to prior loss condition, meaning that you can fully repair the car and have it re-certified and then the salvage brand comes off the title, this only works in non-rollover cases...
i'e re-built tons of totals and had many salvaged vehicles and it's ok for someone like me who just drives them to drive them and not really worried about losing them...but if your average joe and your car is stolen, or picked up in a tornado, your SOL and many people cant afford that type of hit...
it's best in most cases to just avoid the salvage cars unless your capable of taking that risk...
basically salvage cars = good for second/third car but not good for primary...