Your understanding of the settlement is a bit off. If the actual cash value of the vehicle and settlement amount was determined to be $13,000 and you wanted to keep it then salvage value would be deducted from the settlement amount.
Thus if the settlement amount was $13,000 and salvage value is $10,000 then you would be left with the car (which now would have a salvaged title) and $3000. A salvage titled car may be difficult to insure so you might want to search for auto insurance coverage for the vehicle before determining if you will keep the car or not.
To get an auto insurance quote for this or another vehicle you are replacing it with, click here.