What you need to know about a glass cliff and why it could put Twitter's new CEO in danger

The appointment of Twitter's new CEO renewed questions about the 'glass cliff,' a theory that women -- as well as underrepresented minorities -- are more likely to be hired for leadership jobs when there's a crisis, which sets them up for failure.

Less than two months into his US$44 billion purchase of Twitter, Elon Musk declared that whoever took over as the company's CEO "must like pain a lot." Then he promised he'd step down as soon as he found a replacement "foolish enough" to want the job.

That person, Musk announced Friday, is Linda Yaccarino, a highly-regarded advertising executive from NBCUniversal. She'll start in six weeks. How long she'll last might depend on her pain tolerance.

When Musk tweeted on Thursday that he's found a new CEO but didn't say who, one word stuck out: "she." Some of his more extreme Twitter followers took immediate issue with the new CEO's gender, but the fact that Musk hired a woman is actually notable simply because it is so rare -- in business overall and especially in the tech industry -- to see female chief executives.

Her appointment renewed questions about the "glass cliff," a theory that women -- as well as underrepresented minorities -- are more likely to be hired for leadership jobs when there's a crisis, which sets them up for failure. The term was coined in 2005 by University of Exeter professors Michelle Ryan and Alex Haslam, and there have been plenty of famous examples since then, from Yahoo's Marissa Mayer to the U.K.'s Theresa May.

Could Yaccarino be headed toward it?

"Her credentials are impeccable and she's been extremely successful so far. But she's also been in settings where her success was achievable," said Jo-Ellen Pozner, a business professor at Santa Clara University who studies corporate governance. "I mean no disrespect to her or to diminish her in the least. I just think that this is an impossible situation for basically anybody."

Whether or not she succeeds depends in part on how much Musk is willing to step back from Twitter's day-to-day operations. The Tesla and SpaceX CEO said he will continue to serve as Twitter's executive chairman -- Yaccarino's boss -- as well as its chief technology officer, reporting to her. He added that Yaccarino "will focus primarily on business operations."