Can a mod be issued against a closed contract to add funds to enable the contractor to be paid? Can a closed contract be reopened at all?
From your description, it sounds like the government did their due diligence and completed all of the required steps required in accordance with the particular regulations governing the closeout process (See FAR 4.804; DFARS 204.804 & PGI 204.804 for additional details of the closeout process). The fact that the contractor initially verified that all invoices had already been submitted and attested to this by signing the release of further claim asserts your position that you closed the contract out properly. You didn't mention the dollar value of the invoice in question, but I suppose the remedy for the contractor may be to file a claim to try and recover their monies. If you haven't coordinated with your legal counsel on this matter, I'd advise you to do that. Based on the information you provided, it appears the contractor relinquished their rights to submit additional invoices when they signed that release of claim which then prompted you to close out the contract as prescribed in the regulations. In my experience, once a contract is closed out, it is closed out for good although I suppose that doesn't mean that your agency might not be able to find money somewhere to pay for this if they decide to do so anyway.