This is supposed to protect small investors from finding themselves owning shares they can't sell on the market anymore.
The price is set by the equivalent of the SEC.
If that fails to buy all the shares, the company must sell enough stock so that the market is again liquid enough.
I _think_ many countries have similar rules, as cursory googling shows the London stock Exchange changed their minimum free float requirement some years ago.
If they are private person they can attempt to judgement via court and let enforcement authority liquidate their assets or garnish their wages.
There's also requirement (with some exceptions) to make offer to buy publicly listed company's shares when the shareholder's control over the votes increases above 30% and 50%. Normally the price in that case would be the highest price that shareholder paid for the shares during previous 6 months.