The purpose of a lien sale is to recover what is owed for towing and storage. If you surrender the pink slip there will be no need for the expense of a lien sale.
They are entitled to recover the cost of the towing, storage, as well as the costs involved with the lien sale.
If the city (or county) cited you for this, then the ticket is a seperate issue to be settled with whatever government agency it was issued for.
You are responsible for any costs that exceed what they get for the car. Lien sales don't usually get much action, so don't expect to get anything near market value on a lien sale.
As a practacle matter, tow companies don't usually go after additional funds from the owner because most of the time if the owner can't hang on to their car they have no funds to go after. It's the "can't get blood from a turnip" principle.
I would suggest that you take them the pink slip and explane that you can't afford to do anything else and see what happens.
