This may not be that simple and here's why,,,
Towing company A picks up burned out stolen car at the request of law enforcement. (I assume)
OP, is notified that his vehicle has been recovered.
OP learns that recovered vehicle is a complete loss and requests Towing company B to haul the vehicle to the junk yard, which they charge him a fee of $100.00 to accomplish.
Towing company B arrives at Towing company A to pick up vehicle destined for junk/scrap yard and are informed that there are charges accumulated on the vehicle, which must be paid before it will be released from tow company A's yard. (towing and storage already provided by A) These charges have probably already exceeded the $100.00 charge, which tow company B collected to junk the vehicle.
Now comes the guessing part:
Towing company B will claim it was made very clear that the $100.00 fee, was for their time and effort to pick up and haul the car to scrap and that any money already owed to company A, was the car owners responsibility. (This is quite common and many times the customer will pay the bill directly to the company holding the vehicle, or, provide their hired company with the funds needed to release the vehicle) Seeing how this is a common practice, they will further claim that the owner was aware of this and agreed to pay tow company A's bill, so the vehicle could be released. The $100.00 fee, has already been earned by tow company B, when they made the attempt to pick up the vehicle, which was a big waste of time due to the owners neglecting to pay the charges already accumulated on his vehicle, to company A.
So, first off, how did you come to learn that the vehicle was recovered and how did you discover it was burned? If it was through the usual pending lien sale notice sent out by tow company A, it would have taken a week or so for you to become aware of this and the charges would have already exceeded $100.00. I'm guessing you were aware of this when you hired company B to dispose of the vehicle for $100.00.
However, signing the paperwork over to company B was done so they can legally scrap the vehicle as no junk or scrap yard will accept a vehicle without such paperwork. Towing company B was not purchasing the vehicle and never became the legal owners of this burned up hull, it was a total loss. So filing a release of liability with the DMV was redundant, since the car was not operable and only headed for the scrap yard anyway.
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My guess is that you thought you found a way to duck the charges which were already accumulating on your vehicle.
But guess what,,,,, you are wrong and you will now be held responsible for the entire amount company A is billing you for,,,, PAY THEM!
Next time you find yourself in this situation, try working with the tow company who hauled your vehicle into their yard. You could have probably handed the paperwork over to them and paid a couple hundred dollars for their troubles and been done with it. They wouldn't have had to file liens and wait forty or fifty days until they could legally junk the vehicle.