Towing company wants title to my car

So I totaled my car and the insurance is not gonna pay. I paid the towing fees of the tow company who took the car. I tried selling it to numerous places but to no avail, the storage fees itself were more than I would be getting back. The towing company said that if I junked the car with them, there would be no storage fees. So I asked the tow company to junk the car. However, they asked me for the title. What can happen if I do not send the title to them?