If I closed my incorporated sub-contracting business 6 years ago, what liability do I have for a project done 9 years ago that may or may not involve me?

1) Depending on your state and the nature of the potential claim (e.g is for breach of contract? for a loan connected to the project? for negligent construction? etc.) it may well be too late for any claim to be brought. All causes of action are subject to what's called a "statute of limitations," which sets forth the time limit on bringing a lawsuit; once the statute passes, no one can take legal action. Each state sets its own statutory periods, and they vary by the type of cause of action. 9 years, however, is longer than most statutory periods in many states, so it may be too late for anyone to sue.

2) If your business had been an LLC or corporation, then you would likely be immune from any business-related liability unless you personally guaranteed a debt or contractual performance, unless you personally caused some injury or damage (e.g. you were the worker who broke something or crashed a vehicle), or for certain special types of claims (certain tax related claims, for example). If it was a sole proprietorship, however, you could be personally liable for business debts or causes of action.