The only really good advice anyone here can give you under these circumstances is that you must consult with a competent local tax professional immediately. You should be able to get a free or low-cost initial consultation at which you should learn whether you have anything to worry about or not.
On the substance of your question: Employment taxes are the taxes paid for medicare, social security, state unemployment compensation, and withheld income taxes. These taxes are typically referred to as "trust fund taxes" and even if a corporation is the employer, they can be assessed personally against the owners, officers, or other high-level management of the corporation. I can't tell you for sure, but if your ex-husband was secretive about his business, it's possible that he listed you as a shareholder, director or officer without your knowledge. If that's the case, then the state will consider you to be a so-called "responsible person" until you can prove otherwise.
Other than that, I cannot immediately think of a reason why you would be notified if you had no connection with the corporation, which is why I think you should be speaking to a competent local tax attorney tomorrow, or as soon as you can schedule an iniital consultation.
My answer does not constitute legal advice and may not be relied upon by anyone for any purpose and does not constitute an attorney/client relationship or an offer to form such a relationship. This disclaimer is intended to be fully compliant with the requirements of Treasury Department Circular 230 and the terms thereof are fully incorporated by reference. If you wish to consult with me please contact me at dana@nytaxcounsel or visit my website at www.nytaxcounsel.com
You should consult a tax attorney to assist you. In general, you are jointly and severally liable for the taxes payable for the years that you filed a joint return with your ex-husband. However, there are opportunities to remove yourself from this liability such as "Innocent Spouse Relief." You should consult a tax attorney who can help you explore these options.
Andrew B. Gordon, Esq., CPA
Andrew B Gordon is a CPA and attorney licensed to practice law in Illinois. The information provided here is for educational purposes only and is not intended as legal advice for a particular matter. This response does not create any attorney-client relationship with the author. For specific advice about your particular situation, please consult an attorney.
They are probably sending you a copy of the notice because your name is listed on the joint income tax return. You should contact the local IRS Taxpayer Assistance Office. Go to http://www.irs.gov/uac/Contact-My-Local-Office-in-North-Carolina to locate the one nearest you.