Can a former employee sue me for wages after I went out of business?

Yes, legally, you may be sued after you go out of business--going out of business does not terminate the former employee's legal rights, or deny him/her a cause of action.

If the business had been a corporation or LLC, then practically, you may have nothing to worry about: as a general matter, only the corporation or LLC may be sued, and if it has been dissolved--or even if it still exists, but has no income or assets--the employee will not be able to recover anything. The corporate of LLC form insulates the owner(s) from the vast majority of potential liability.

However, if the company was a sole proprietorship or partnership, then the owner(s) may be sued personally for unpaid, etc. wages.