The answer is yes, they can. Whether they will achieve their goals of they do so is another question. A plaintiff can always try to pierce the LLC corporate veil by holding you personally responsible by theories such as negligence or gross negligence.
It all comes down to the the amount at stake: if you your personal net worth is big enough, and there is a reasonable chance that a judge may follow the “personal liability” route, a contingency fee attorney may give it a shot.
This said, I fully agree with attorney Brinkmeier. If you went by the book and did proper bookkeeping, kept personal and business accounts separate, it will be much more difficult to go after you as an individual.
Douglass Lodmell is the nations #1 Asset Protection attorney and has clients in all 50 states, protecting over $4 Billion in client assets. Answers given by him in this forum do not establish an attorney-client relation. He advises to seek a specialized attorney in the area of your interest for legal representation.
Both of the previous answers are correct to some extent. The chief reason for using the LLC structure is to limit personal liability, and keep the debts focused on the business. There are ways to "pierce the veil" of an LLC, which may or may not apply in your case, and will depend greatly on the facts surrounding the operations of the business and the way the debt was acquired. This is the object of Mr. Brinkmeier's comment about following the formalities. This area of law is very complex, and very fact specific. An attorney will need to know the full details and consult with you to give a complete answer to this piece.
There is a second risk for liability when you close a business, which relates to how the assets of the business are distributed. In a nutshell, if you took money out when closing the business, and you knew there were any outstanding debts, then that money can be taken back from you. Because you hint that there was a judicial case which resulted in judgment, there are additional details which should be addressed to give a complete answer. I encourage you to consult with an attorney on this issue.
This answer is offered as a public service for general information only and may not be relied upon as legal advice.