It's a private firm, and the voting example I gave isn't really that good.

A more reasonable case is that they can heavily influence what contractors and 3rd parties are used for projects. Not something that needs a board vote, but something a 40% shareholder has a lot of say in.

I imagine they don't hold a vote on whether to put backdoors or not on a board meeting. So that raises the question. If not like that, then how does it actually happen?

You just go to the executives and point out that you own 40% of the ownership, and you'd really like them to hire these couple of guys and put them on this team, and then not ask too many questions about what they're doing, or you'll use your 40% ownership to make their lives more difficult, which at 40% can easily involve ousting them personally. (See other people's comments about the difficulty of getting enough voters to actually vote to prevent a 40% stake from being the vote winner.)

The literal thing I just said isn't even that unethical; suppose you own 100% of a company, then telling it to hire someone specific and pay them this much and put them here would be fully within your rights as owner. (There's probably a legal hurdle or two to clear, but AFAIK it's nothing that will actually stop you.) How that changes ethically as your ownership stake decreases I'll leave as an exercise for the reader. What's unethical is what they'll be doing when they get there, and who else is tainted ethically depends on how much they know and what they do about it.

The other examples are public companies. Epic Games isn’t. Something shady could still happen but there are only a few shareholders that control the vast majority of the company. I think a few other firms and the founder.

A bit too legion of Doom in retrospect.

But you would get to heavily influence what contractors and vendors the company works with are good vectors.

As well as partnership and integrations.