Of course the company wouldn't meet the listing requirements but...

Of course the company wouldn't meet the listing requirements but that's irrelevant. There is probably something in the corporations act saying there must be at least one shareholder. But in theory as a company is legally esentially a person I can't see any reason why a company couldn't own all its own shares. Would be like an incorporated asociation but with a profit motive and only management - no members.

Or would it become a zombie company!