When its not possible to fire a CEO that hold equity in the company?

The amount of equity one holds in a company has nothing to do with being possible to get fired as a CEO. But it does help.

In Mark Zuckerberg's case, Facebook has two classes of stock: Class A shares that carry one vote apiece (the same shares you can buy on the stock exchange), and Class B shares that carry 10 votes per share. Zuckerberg has a boatload of Class B shares and, as a result, controls roughly 60 percent of the voting power at the company.

According to SEC Filling: Statement of Beneficial Ownership Mark Zuckerberg owns 29.3% of Facebook’s Class A shares, but only around 20% of the company as a whole. That makes this stake worth closer to $13.6 billion rather than $18 billion. In addition to that, Zuckerberg owns other types of shares, harder to track. So his total stake is worth more than that."


For further understanding please read this Re/Code article: How Can Mark Zuckerberg Give Away All That Stock and Still Control Facebook?