Yes, of course they can. Especially if the suit pertains to back payroll or other taxes owed. In general, and as my colleague noted, they are protected if the activity is within the regular course of business such as general business contracts, disputes, etc and the courts will not pierce the corp veil absent a really good reason.
I suggest you discuss your situation in private with a lawyer to flesh out all the details. Most of us here, including myself, offer a free phone consult.
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Absent clear and convincing evidence of outright Fraud in business dealings, the answer generally is NO. The Board of Directors (who are elected by the Shareholders) set policy. The officers carry it out. Liability protection is the number one reason for establishing a Corporation in the first place. Moreover, as to payments, the company cannot deduct compensation to workers without keeping documentary proof of corporate expenses. I'd recommend you sit down with a New York licensed Business Law attorney and go through your concerns and map out a pathway going forward. Good Luck!
It depends of the facts.
I am a former federal and State prosecutor and now handle criminal defense and personal injury/civil rights cases. Feel free to check out my web site and contact me at (212) 577-9797 or via email at Eric@RothsteinLawNY.com. I was named to the Super Lawyers list as one of the top attorneys in New York for 2012. No more than 5 percent of the lawyers in the state are selected by Super Lawyers. The above answer is for informational purposes only and not meant as legal advice.