One possibility. The car is totaled. Then you buy it back for like $3000, put some of the insurance money into fixing it with salvage/used parts. You'll be pocketing some money, but driving a car with a salvage title.
But it's between you and the adjuster at this point, but you should think about a best case scenario--a big payout/fixing the car, non totaled/buying it back as salvage--and work toward that goal.
I'd suggest the NOVA's Ask an Insurance Adjuster Anything thread. Helped me hugely when my touring was totaled.