Theoretically, the tow service could send your debt to collections, i.e., the difference between the auction value of the vehicle and the amount of your bill. Then, you would have to dispute the debt, and force the debt collector to sue you -- which it probably won't. It will just ding your credit report
. You can offer the debt collector perhaps 10% of the original bill, and settle the matter, or you can tell them to "stick it," and see if they sue.
Debt collectors rarely sue to collect a judgment, unless they know that the debtor has the ability to pay and is not likely to file for bankruptcy protection -- which will discharge the debt entirely.
Anyway, I understand the gamesmanship here. Each day the storage charges increase by an absurd amount. There's no way that it costs the tow yard $200-$300 to park a car in its lot, and no court would find such charges "reasonable."
Anyway, that's how it all is likely to shake out.
Hope this helps.