I get this a lot. Someone is involved a car crash. The insurance company for the other side tells them the car is a total loss. They are sure that they want to keep their car. I am sure they do not want to keep their car.
First, before you take the insurance company's word for it, do a few things. Go to a reputable, independent shop and ask for an estimate. It is not uncommon for the insurance company to call the shop and tell them that if a car is close, they want to make sure it is a total loss. So, go get your own estimate. Of course, you should be doing this anyway, even if you are going to have your car fixed. After you get an estimate, figure out what your car is worth. Do not take the insurance company's word for it. For a small fee, I assist people in determining the fair market value of their car and preparing a declaration. Just email me and find out about it!
Second, once the car is a total loss, and you are sure of it, give it to the insurance company. Get rid of it! Why, you ask? If your car is declared a total loss, it is reported to the DMV. You end up with a salvaged title. Try selling a car with a salvaged title. And try insuring a car with a salvaged title. Yes, you can clean up the title, but it is a painstaking process that will require many, many hours. Finally, the car is never going to run the same, feel the same, or be the same. Get rid of it!
I know many people are sentimentally attached to their cars. I am. But, once your car is a total loss, you are much better off getting rid of it and finding yourself a new car!