Well, as long as shares of a corporation's stock were still in existence, it would still have 'owners'. As things stand, though, that is a meaningless title already.

Shareholders have nothing to do with the operations of any publicly traded corporation. They are not legally responsible for anything done by the corporation. They can suggest and protest concerning the broadest issues--mostly 'social issues'--but so can the general public.

The senior executives (in theory, overseen by a board of directors), make all the determinative decisions for the business. Those positions would still exist. There is no reason I can see for the business to cease to exist even after all its stock did cease to exist.