It will not owe tax if the taxes were included in the discharge debts. Even if the corp still owes the taxes, the IRS will never be able to collect it since you say the company is shut down. They cannot come after the owner of the corp personally if the taxes owed are income taxes. If the taxes are 941/trust fund taxes, then they would not be dischargeable in bankruptcy and the IRS would be able to go after you personally for those taxes.
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I agree with the prior attorney on all points. Also note that in certain states you cannot "shut down" or dissolve a corporate unless you do something called "winding up" the corporation, which involves: 1) Paying of creditors and 2) Paying all franchise taxes. States like California make this a precondition to dissolving but states such as Delaware allow you to dissolve the corporation first, but keep it alive for 3 years following the dissolution to perform the "winding up" process in which creditor can sue the corporation -- Texas likely has a similar law.
You may want to therefore declare bankruptcy instead of "shut down" the corporation if you will not be able to pay of all 3rd party creditors and "wind up" the business. I agree with Mr. Tomas that all of the debts should be discharged by the corporation and not affect your own personal assets unless they are payroll taxes that you failed to pay (941/"Trust Fund" Taxes). If these taxes are included in the corporate bankruptcy, then they should no longer exist if they are part of the bankruptcy plan.
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I have a little different take on this than the prior answers. An S corporation very rarely owes income tax. The whole point of creating the S corp was so that the profit and loss would flow through to the shareholders like a partnership but still have the limitation of liability features of a corporation. It is not impossible for the S corp to owe taxes, but highly unlikely. If the corporation does owe taxes than I agree with the prior answers about the liability being discharged in bankruptcy. In Texas a corporation does not go away unless it is formally dissolved. If you did not file required franchise tax returns with the State of Texas in all likelihood the State forfeited the charter of the corporation. Unfortunately in Texas once that happens, the officers and directors are personally liable for the debts of the corporation until the charter is reinstated. Confusing. You should contact competent counsel.