Though the chances of an ouster are slim, the fact that it has even come up shows the extent of Facebook's and Sandberg's troubles.
"Her brand was being manicured with the same resources and care as the gardens of Tokyo," said Scott Galloway, a New York University marketing professor.
"And unfortunately a hurricane has come through the garden."
Facebook has been dealing with hurricanes for the past two years : fake news, elections interference, hate speech, a privacy scandal, the list goes on.
The company's response namely, Zuckerberg's and Sandberg's has been slow at best, misleading and obfuscating at worst, as The New York Times reported last week.
That report, and one from The Wall Street Journal , underscored Sandberg's influence at the company, even as Zuckerberg has borne much of the criticism and anger.
As chief operating officer, Sandberg is in charge of Facebook's business dealings, including the ads that make up the bulk of the company's revenue. She steered Facebook from a rising tech startup into a viable global business expected to reap $55 billion in revenue this year. The company is second only to Google in digital advertising.
But she's also gotten the blame when things go wrong, including Facebook's failure to spot Russian attempts to influence US elections by buying US political ads in rubles.
Though Sandberg has denied knowing that Facebook hired an opposition research firm to discredit activists, she created a permissive environment through what the Times called an "aggressive lobbying campaign" against critics. Facebook fired the firm, Definers, after the Times report came out.
Facebook declined to comment on Sandberg or make her available for an interview.
A representative instead pointed to Zuckerberg's remarks that overall, "Sheryl is doing great work for the company. She's been a very important partner to me and continues to be, and will continue to be. She's leading a lot of the efforts to improve our systems in these areas."
Sandberg, 49, who was hired away from Google in 2008, has been a crucial "heat shield" for Zuckerberg, as Galloway put it, as lawmakers and the public crank up criticism of the 34-year-old founder.
In September, Facebook sent Sandberg to testify before the Senate intelligence committee, eliciting a warmer response than her boss did three months before.
Sandberg, former chief of staff for treasury secretary Larry Summers, appears more comfortable in Washington meeting rooms than Zuckerberg, who can seem robotic.
Her profile is high enough that lawmakers don't feel stilted when she shows up. She's written (with help) two books, including 2013's "Lean In" about women and leadership.
Her second book, "Plan B," is about dealing with loss and grief after her husband died unexpectedly. She was the lone chief operating officer among a who's who of tech CEOs including Apple's Tim Cook and Amazon's Jeff Bezos to meet with Donald Trump a month after his election.
"It's both who she is and how bereft Silicon Valley is of strong, powerful female voices," crisis management expert Richard Levick said.
"She has positioned herself as one of those strong voices with 'Lean In.'" But her high profile also makes her more susceptible to criticism.
The chorus for Sandberg to leave is getting louder. CNBC commentator Jim Cramer predicted Monday that Facebook's stock would rise if Sandberg leaves or gets fired. NYU's Galloway believes both Sandberg and Zuckerberg should be fired for allowing Facebook to turn into an entity that harms democracy around the world.
"Every day executives are fired for a fraction of infractions these two have committed," he said.
Besides elections interference, Zuckerberg and Sandberg have been criticized for their slow response to the Cambridge Analytica scandal, in which the data-mining firm accessed millions of users' private information without their permission.
The pair were silent for days after the news came out. According to the Journal, Zuckerberg told Sandberg this spring that he blamed her and her teams for the "public fallout" over Cambridge Analytica.
Citing unnamed sources, the newspaper said Sandberg at one point wondered if she should be worried about her job (though that appears to no longer be the case, based on Zuckerberg's public support).
Because of the way Facebook is set up, firing Zuckerberg would be all but impossible. He controls the majority of the company's voting stock, serves as its chairman and has at least publicly the support of its board of directors. Essentially, he'd have to fire himself.
Firing Sandberg would be the next logical option to hold a high-level executive accountable, but Galloway also doesn't see this happening.
For one thing, he said, it would look bad to fire one of the only top female executives in an industry where women "face inordinately high obstacles to get to leadership positions." Beyond that, Sandberg has also been a positive force on Facebook.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)