The Insurance Company most likely will want not to fix the Car but total it. However, in California if you want the wreck I believe the Insurance Company will let you have it but will deduct what a Junk Yard would give them for the Car from the amount they pay you.

But, you need to ask them; they are not going to suggest it.

The Car is given back to You as a Salvaged Car and if you fix it and run it when you register it will have Salvaged on the Title (again here in CA).

I have read of people saying that you can make the Insurance Compan Fix the Car but I have no details on that being so.
I am guessing that they are only going to fix up to a certain financial amount. After that you would be on your own.

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84 300D, 82 Volvo 244Gl Diesel