If you run a business then you take responsibility for its operations. There are a range of legal requirements that directors have to conform to as well as duties to fellow directors, customers and suppliers.
Directors can be held personally liable for any mistakes that they make even after the business has closed. In fact the duties of a director are so onerous that the estate can be left to foot the bill after the director has died.
It is important to remember that duties of directors apply to non-executive and executive directors alike. You do not need to own shares in the company to be responsible for the actions that your fellow directors take. Your liability can extend even after you leave the business.