You should be speaking with a local bankruptcy attorney to explore your options. So long as the corp was in good standing and there does not seem to be any reason to believe that it was used as an alter ego company and all the debt you refer to is in fact company debt then I see no reason why the principals should fear being personally liable for it.
You are correct that the state will not allow you to just dissolve the entity until the resolution of its debts is reached. Dissolution however is really not your priority here. You need a proper winding up which will likely mean a bankruptcy filing for the corp. You will need to liqudate any and all assets, etc.
Again, discuss this over with a lawyer in private. Most of us here, including myself, offer a free phone consult.
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You have a few different issues here:
In determining whether you are responsible for the debt individually or not, you have to look at how the documents were signed and if you personally guaranteed them. If you did not personally guarantee them, the subcontractor would have to prove that they were not corporate debts in order to collect from you individually. This can get expensive.
If you don't file the annual report and pay the filing fee to the secretary of state, the secretary of state will dissolve your corporation.
Even if you are not personally responsible for the debt and the secretary of state dissolves the corporation, there could still be tax liability or licensure issues. Make sure all your taxes are paid with Lee County and the IRS. If there are payroll taxes owed, the IRS can come after you personally. Also, if your subcontractor can prove fraud, he might be able to file a complaint with the Construction Industry Licensing Board.
You should probably consider a bankruptcy consultation to look at categorizing each debt.
You have two other thoughtful answers, and I'll add something different: Personal liability to officers can arise if the company is "insolvent" at some time and the officers pay out the last funds to themselves or shareholders which results in insufficient money to pay creditors. This can be a complicated analysis, but if you seek legal advice you should look for an attorney who handles matters for small corporation owners that involve personal liability claims.
Also, as far as bankruptcy is concerned, a bankruptcy attorney should tell you that corporations do not get a "discharge" (relief from their debts) in bankruptcy, so there may be no benefit to filing one. Proper winding down of the company's affairs is what's needed here.
It is not uncommon for entities to allow themselves to be administratively dissolved by the State by simply by not filing an annual report. I agree with others that the issue of whether directors or others might be liable for unpaid corporate obligations is a very fact specific analysis and requires a detailed understanding of the debt itself, any distributions or payments made to other creditors and shareholders and a litany of other factors.