Shareholders can put pressure on the board to fire the exrcutive. If they don't, that means they're fine with the situation.

As a shareholder in many companies, I cannot put pressure on a board, and I'm mostly unaware of how they are internally managed.

Shareholders are basically fine with fraud as long a they benefit in the end .

What fraction of ownership would make it okay?

100% ? 50% ? Something in the middle?

50% + 1 share.

Even in the family business, there should be limits. What if the family business becomesand empire worth >20% of a contries GDP - e.g. Samsung. It is absolutely not reasonable to pass this amount of wealth to children of the founder.

Samsung is a public company no? It's not family-owned as far as I can see.

This is correct money-wise. Samsung Group's market cap is around $400-500 billion, while its chairman (the family head) is estimated to be worth $10-15 billion.

It's not as correct decision-making influence-wise. The power balance of "family vs remaining shareholders" is different from what would be assumed purely based on those numbers.

It can be said that Samsung C&T is the actual head subsidiary/control vehicle through which the other subsidiaries are run at the top level, and the family is easily the biggest shareholder in C&T.

The KOSPI, which is what the subsidiaries are listed on (the "group" is not listed), is seen as a bit of a joke by both foreign and domestic investors for that reason. Besides its obvious downsides, it does have upsides as well - the "sacrifice everything for the short-term stock price" that is the norm in the US is less common in Korea for this reason. Corporations work differently.

Samsung is not a family business in the legal sense of the term: it has shareholders and is thus nominally accountable to the public.