The same would likely occur should any Facebook directors begin to publicly criticize Zuckerberg or voice support for any shareholder lawsuits or proposals, such as Trillium Asset Management's proposal for an independent Facebook board chairman, that could diminish the Facebook co-founder's control of the company.
Zuckerberg "has the right to remove them from office tomorrow," said John Coffee, director of the Center on Corporate Governance at Columbia Law School.
"There's nothing they can do," said Charles Elson, the director of the John L. Weinberg Center for Corporate Governance at the University of Delaware. "Their role is symbolic and that's it."
They could quit dramatically, but investors probably wouldn't care.The board could make a symbolic move and quit en masse. A dramatic resignation would cause more headlines for the company and increase pressure on Zuckerberg.
But many of the experts who spoke with CNBC said they were skeptical that the company's directors are held in high enough regard by Facebook's investors to cause substantial damage.
"No one focuses on that board," Elson said. "They focus on Mark Zuckerberg because they know he controls the company."
A lawsuit would be impossible to win. The directors could also theoretically choose to pursue a legal route and sue the company or Zuckerberg on some kind of fiduciary claim, said Elson, but that type of move is highly rare and would get messy. None of the experts CNBC spoke with expect this to happen.
Last year, Facebook scrapped plans to change its stock structure after Stuart Grant of Bench Walk Advisors sued the company.
But Grant thinks a lawsuit to remove Zuckerberg from the board would have no chance. "You can criticize him all you want, but it is not illegal to not do a good job," he says. "There is no lawsuit."
About the only thing Facebook's directors can do is reason with Zuckerberg, the experts said. Besides that, there really aren't any options.
"If Zuckerberg wants to stay chairman then Zuckerberg is going to stay chairman," Grant said.
Thus far, Zuckerberg has shown no interest in giving up his chairmanship.
Last month, when asked if he would step down as chairman, Zuckerberg told CNN "I'm not currently thinking that that makes sense."
I quit Instagram and Facebook and it made me happier — and that's a big problem for social media companies