Ann: Bidder's Statement from Hancock Prospecting Pty Ltd, page-5

Holders of the 25% become known as Minority Shareholders.
It is not a good position to fine oneself as it results in a loss of control and no ability to sell your shares as they will have been delisted from the ASX. You become locked in, unable to sell.
Gina would have the power to do whatever she wants to do within the law with the assets of the company.
Examples of this in the past have lead to loans being made to other companies, assets being sold for less than their true value
Given the wide share register of AGO, the scenario is not necessarily "unlikely" as you have put it, although usually the acquirer does not want to go down that path, as their are additional costs of reporting to the remaining members that they would prefer not to have to do.

If Gina gets 90% then she can compulsorily acquire the remaining 10%