Whoever is buying the company makes an offer, it can get negotiated by the company/board. Once the negotiations are complete, they can put it up to a vote. Don't overthink this too hard, its not as strange a transaction as you may think.

There are some outlier situations where a certain large shareholder may not get to vote if they have a conflict, but not always. Even as the majority holder, well, in many cases, of course being the majority holder means you can make the decisions, even to sell.