Going theory is that he was a former director or CEO. I think figuring out who he is and how he got the shares is going to be the more interesting story that's going to cause some drama. Your average player couldn't have pulled this off because of how shares work.
Would it have been possible they were given shares by another player inside the corp that does have shares? Although I'm sure share transactions are logged and public information, if not through the game then through the APIs, and most Corporations will make some API access required.
you have to be trusted somehow to gain access to these shares in the first place. thou afaik they were never important for anything else than showing of.
Using shares to gain control of someone elses corp and steal their stuff is an extremely old scam. Like, it was very well understood some 15 years ago. The mechanics haven't changed.
I don't remember the details well, it was a long time ago, but there was a step by step guide to stealing a corp away. You had to have roles. I got them via the standard alliance recruitment "need a temp director to run a full corp check via api". Believable, and 24 hours later the corp was mine along with all its assets (a lot less than this).
I don’t know anything about EVE though.