These days the vast majority of executive comp is in stock - imagine if bad optics could force you to take a 60% pay cut, you'd be pretty conservative with your choices.
If a too good offer comes by, for instance, for one to buy Google:
the offer has to be disclosed; and regardless if the founders like it or not -- or what the voting majority says, there is a price where the remaining shareholders can force Google to be sold.
If too many of them do, the stock goes down, and essentially everyone at the company (especially the executives) take a pay cut. The executives aren't even just thinking about their own pay. The entire company's ability to attract and retain talent depends on the stock price going up.
1. Duty of Care
2. Duty of Loyalty
3. Duty of Disclosure
4. Duty of Confidentiality
5. Duty of Prudence
6. Duty of Good Faith
You can start looking at this rabbit hole here (and it is a rabbit hole): https://www.law.cornell.edu/wex/fiduciary_duty
P.S. Just a (fly-by)comment; not advice of any short or kind -- either investment or legal. P.S.2 Oh it does happen that share/stake holders seek enforcement for breach of fiduciary duties. I would say it is quite common.
As far as I know the only duty a company has towards shareholders is "protect them" (aka: don't mess up and make money). As long as the company eventually does that there is no issue. Even if it takes 8 quarters to become profitable (or 10+ years, see Amazon).
There are probably ways in which shareholders can get together and request something (in court?), but that almost never happens? Maybe I'm wrong. If so, would love to see examples.