Carlos Ghosn was on the top of the automotive industry world. Simultaneously head of Nissan Motor Company, Mitsubishi Motors, and Groupe Renault one day. The next, detained for under-reporting income.

He's not the only chief executive who got caught with an inner bad boy. Uber co-founder Travis Kalanick was pressured to resign after too many reports of the company's sexual harassment culture. Papa John's no longer has John Schnatter as its face after the racial slur incident during a conference call. Critics have called for Mark Zuckerberg to at least step down as Facebook's chairman.

Most CEOs do their work and stay out of the public eye. But some won't. It's almost as though they consider themselves reigning royalty.

That's about the gist of it, according to Yale management professor Jeffrey Sonnenfeld, an expert on leadership and governance. Such "monarchic CEOs...believe there is one indispensable person," he told NBC News. "They have a heroic mission and are driven by this need for immortality through their work and a separate drive for heroic stature. They don't have other interests. It's all the job."

Sonnenfeld says between 6 percent and 8 percent of public companies have problem CEOs who feel they should be able to do as they wish — and then set things up to make it difficult to be replaced. "They often have undermined potential successors," said Sonnenfeld. By the time a crisis arises, the board feels trapped, that they have no leverage."

A CEO in this mold who is highly successful may find that investors and the board of directors are first welcoming. But there's no guarantee that the good times will continue.

"They should make the same disclaimer of CEOs as they do for mutual funds: Past performance is not a predictor of future performance," said Nell Minow, vice chair of ValueEdge Advisors. When entranced early on, a board may agree to provisions that literally put a CEO above the law. According to Minow, former Tyco International CEO Dennis Koslowski had a clause in his employment contract that said a felony could not be a cause for termination unless it was directly connected to the company's operations.

Disgraced entertainment CEO Harvey Weinstein, when he ran The Weinstein Company, reportedly had a clause in his contract that gave him an out for sexual harassment claims, according to TMZ. By paying significant damages to the company, he could stay out of trouble if he "treated someone improperly in violation of the company's Code of Conduct."

Ultimately, the CEO works for the shareholders through their representatives, the board of directors, who are supposed to provide oversight.

However, the chief executive has extraordinary influence over who serves as directors. "It's very hard for the board to really provide oversight and monitoring, and it's especially hard if the CEO is also the chair of the board," as Ghosn was, said Margarethe Wiersema, professor of strategy at the University of California, Irvine Paul Merage School of Business. The CEO/chair also controls the board's agenda and information it receives.

The biggest aid, Minow said, is to change the law so that shareholder votes on directors would be binding and not something the board could ignore. "There was one case where all nine directors at a company failed to get support from the shareholders," she told NBC News. "They turned their resignations in to each other and then they refused them and continued to serve. This was something we tried to get into Dodd-Frank [financial reform bill] unsuccessfully."

And it's unlikely that the case of Ghosn will suddenly change things.