Even if they travel with the property, you can rest assured that the Buyer is not interested in paying your fines, unless it is a really good deal for them. Deal with it up front wit hthe Buyer and the Buyes's Attorney.
This is a legal question so you should seek council from an attorney. My experience has shown me that such a fine is usually made out to you personally, so you would still be responsible for clearing it. If it is a judgment against you then it's attached to the property and would be paid at closing to clear title prior to the sale of the property.
I agreed with Suzanne, you need an Attorney in this case. As for the Fines, those are your responsibility. Take care of them 1st, and everything eles will follow. Buyers are looking for good deals not headaches. Elba Adorno, Resltor, PFR, Hamilton, NJ
Are you using an attorney for the closing? You should be. The bank usually pays the attorney. I know tax liens have to be paid. In fact, all liens will have to be satisfied prior to closing somehow. Fines imposed by a court may be treated differently. I suspect this question is so specific that only an attorney will be able to provide you with an answer.