I don't know if she appeared in court at the time or if it was a default judgment.
Bottomline, though, she really could not prove that she had sold the vehicle prior to when it was involved in that accident. Since the vehicle was not insured, she got tagged with allowing "her" vehicle to be operating on the roads without the proper insurance and then not paying for the damage that arose from the accident that was deemed to be the driver's fault. The only way for her to get her license back is to pay that judgment and/or probably comply with some other DMV conditions.
Anyone can get have an accident and then claim that the vehicle was sold to someone else before the accident happened so it is really that person's fault. Her story may sounded like the oldest story in the books, if she told it to the judge.
Since there was no insurance and the damage was not paid for and she allowed "her" vehicle to be driven on the highways without insurance, the Dept of Motor vehicles suspended her license. It may have suspended the buyer's license as well. It is almos automatic that if someone has an accident in "your" vehicle and there is no insurance, your license gets suspended until you pay the judgment.
As noted, this was a hard lesson to learn. Selling a vehicle is not as simple as holding a garage sale where you sell your old sticks of furniture and children's outgrown, but useable clothing. She appears to have not known that she needed that documentation, such as a bill of sale, or that she needed to report the sale to the DMV for her own protection. Because of her ignorance she got burned big time.
Ignorance of the law, however, is almost never a valid "excuse" and the judge may not have "bought it". But, even if the judge personally did believe her, her failure to follow the proper legal steps when the selling the vehicle probably left the judge little choice but to find against her.
To the Original Poster. I am afraid this matter is a done deal and I doubt that there is much legally that you can do to get the judgment set aside. The judgment almost certainly holds both you and that buyer equally liable for the entire amount. The person holding the judgment is free to pick and choose who to chase.
It is not a situation where you get to pay half of the amount owed and the law firm gets chase that buyer for the other half. You probably are on the hook for the entire amount. However, if this law firm bought the debt from the original creditor, you probably can settle it for less the the total amount owed because the law firm probably did not pay full face value for it.
If your tax refund will not cover the possible cost, then you are going to have to get "creative" in coming up with the rest of the money. I would not rule out the possibility that further negotiation might result in you maybe having to pay less than $1500. On the other hand, that law firm probably knows that you are not contacting them solely out of the goodness of your heart and that you want your license back. That does give them some leverage. Still, if this accident happened in 2006, this debt is getting old and has not produced much in the way of results in the last six plus years. You might be able to shave a couple hundred off the initial settlement figure. But, don't burden them with your sob story. Debt collectors hear these stories day in and day out and generally are not impressed.