Can I keep my damaged car and get paid actual car value

I have been offered a settlement value for my totaled car it is a 2009 toyota camery with a little over 12,000 miles on it this is in Florida . They offered me a little over 17,000 but i think its worth more than that can I take the 17,000 and tell them I want to keep my damaged car also so I can sell it to salvage myself? They said they cant give me a check until I give them my title. Ive been with them paying premiums for sometime I am paying them to protect me in case of a total loss not to lose my car then offer to give it to them once they pay me for my loss. Example if you own your house if a hurricane damages it really bad you paid your premiums to have another house rebuilt and thats what they pay you for, not to have or keep anything of your home that they may be able to sell. So can I keep my car which, I cant understand why I couldnt ,and get paid for what the actual car value is.