Typically after the settlement is paid for a vehicle that is found to be a total loss the damaged car goes to an auction or salvage yard, where it is typically auctioned to the highest bidder and used for parts. The insurance company keeps the proceeds of this sale.
If you want to keep your damaged vehicle, some insurance companies will forgo the auction process and turn the car over to you (usually in cases where the car is over 10 years old). They will still have to pay you the actual cash value of the car, but may deduct the amount the car would have brought at auction (salvage value); this is buying the vehicle back.
It will depend upon state laws if you can buy back a vehicle from an insurance carrier once they have declared it to be a total loss. For example in Illinois one cannot normally keep a vehicle after it has been declared a total loss. The Illinois Vehicle Code does not permit you the right to retain the salvage once the insurance company has deemed your automobile a total loss except for a couple of exclusions. These exclusions are:1) if the vehicle has incurred only hail damage that does not affect the operational safety of the vehicle, or 2) if the vehicle is nine (9) model years of age or older.
Now if your state does allow vehicles that have been totaled out to be bought back by individuals (and then given either a salvage or rebuilt title) then it would next be up to the guidelines of an insurance company whether they would sell you back the car and how they determine the salvage value of the vehicle.
Many insurers will allow you to "buy back" a vehicle they have totaled out if you wish to repair it and make it roadworthy again. If your insurer allows you to do this, you will have to inform your insurer right away if you want your car back. Once it goes to the salvage yard, you will have little chance of getting it back, since only licensed auto salvagers are normally allowed to attend these auctions.
Now the salvage value that you would owe the insurance company (or have taken out of the settlement amount) is determined by the insurance company. There is no universal list for how much salvage value would be on any certain car, it depends upon the car and its damages and how much it is worth in its current state after being found a total loss.
In general salvage value is the amount of money the insurer would recoup when selling the vehicle through a licensed salvage vendor. So instead of selling it to a salvage vendor they are allowing you to buy your car back, get the needed repairs and drive it again.
So the buy back amount (salvage value) is the worth of the car in the condition it is in with the damages it sustained in the accident. If you wish to buy back a car from an insurance company that deemed your vehicle a total loss you should discuss the value of the car and the cost to buy it back. You can check around with local salvage yards to make sure the salvage value the insurance company quoted you seems correct for your vehicle.
Even if your insurer allows you to buy back the car, it may not be worth the time and expense to get it back on the road if your state has a number of special requirements you must satisfy (e.g., buying a salvage title or having the car inspected by the state police after it's been repaired). Also, some insurance companies will not insure vehicle with a salvage title so it may difficult to find insurance for the vehicle it now that it has a salvage title on it.