My car got totaled in a crash and the auto body shop wants keep it for nothing in return. Is that normal?

So, I got into a car crash where my Honda Fit had its airbags deployed. The cops came and had it towed away before I really had a say. The auto body shop said they would see if they could fix it. I got a call saying because the airbags were deployed, it would cost more to repair it than to just buy another car. It's accruing charged just having it stored there. I thought they would be willing to give me a few hundred dollars for it as scrap. Instead they want me to give them the title and pay the $250 towing/storage fee for nothing in return. I'm not really familiar with this kind of stuff, but my gut tells me it's unfair. What should I do?

Added (1). I only have liability insurance.

Added (2). I was at fault. I don't know if that's relevant.

Did you have collision insurance? If so, that should have been where you got money for your totaled car from.

If you lacked such coverage, then you are out of luck. You should have discussed such terms with the body shop earlier.

Andre L has it correct.

OK, so either pressure them to waive the towing and storage in exchange for the title, or pay the towing and storage fee, and pay to have the car brought to your house (or a friend's house) then start parting it out to try and recover some money and then sell the carcass to a scrap metal dealer. If you have nowhere to put It so you can do that then just walk away and learn to drive ore safely and carry collision insurance.

EPIC FAIL

What does your insurance company say? If they paid the claim, the car belongs to them if they totaled it. Check with your local scrapyard to see what they would give you for it.

With only liability insurance, you're on you're on your own with cost of repairs. And the shop is almost certainly right about the cost of repairs when airbags have been deployed. I would say don't pay the shop anything, let them have the car to sell for whatever they can get for it. If you still owe money on a loan for the car you will need to pay off that loan, in full, immediately.

Offer them the title in lieu of ALL charges, they should take it. Their only recourse is to file a mechanics lien to get title to sell or get rid of the scrap and they can't come back to you for charges. You did not ask them to toe or store it the cops did and they have a contract with the towing outfit.