LOS ANGELES — Lots of corporate chieftains have golden parachutes, but it’s rare for them to be triggered when another executive takes the fall. That could happen at Viacom Inc.

Chief operating officer Tom Dooley could head for the exits and leave with about $63 million if controlling shareholder Sumner Redstone sacks his boss, chief executive Philippe Dauman, and doesn’t offer the top job to the COO.

Last week, Redstone’s lawyers said the mogul is weighing changes to Viacom’s leadership and board.

Meanwhile, Dauman, said Thursday that the entertainment company was continuing its efforts to sell a stake in Paramount Pictures but that it would miss its June target for reaching an agreement for the film and television studio.

Speaking at an investor conference in Manhattan, Dauman said that “naturally, recent events’’ had slowed the sales process.

He was alluding to the internal and external turmoil engulfing Viacom, which owns Paramount.

The ailing 93-year-old mogul Sumner M. Redstone has said through representatives that he disapproved of a deal for Paramount, referring to the studio as his “baby.’’ Redstone controls about 80 percent of the voting shares in Viacom and CBS through National Amusements, the private theater chain company.

On Monday, National Amusements disclosed that it had changed Viacom’s corporate bylaws to prevent Viacom from selling any part of Paramount without unanimous approval of Viacom’s board, effectively holding up a potential sale. A Viacom spokesman called the actions “illegitimate,’’ stating that they had stemmed from “invalid changes’’ made in May to the National Amusements board.

Golden parachutes put a tangible price on the tumult rocking Viacom’s executive suite as Redstone reasserts control over the parent company of Paramount Pictures, MTV, and Nickelodeon. Dauman, who is challenging Redstone’s mental capacity in court, has an even more lucrative severance benefit of almost $83 million, according to data from the company and the Bloomberg Pay Index.

Redstone, who also controls CBS Corp. through his Massachusetts-based National Amusements Inc. theater company, is known for the rich salaries and bonuses he pays his top executives. Dauman, 62, is routinely among the highest-paid US media executives. His $35.7 million in compensation last year made him 41st overall among 200 executives tracked by Bloomberg. CBS’s CEO, Leslie Moonves, earned $46.1 million last year to place 26th.

Dooley’s contract includes a “good reason’’ clause that lets him leave with three years’ compensation if he isn’t offered the chance to succeed his boss. That would amount to $63 million, including prorated salary and bonuses, benefits, and stock and options awards, according to Viacom and the Bloomberg Pay Index. The company’s number two executive, Dooley could also depart if he’s ­removed as a director.

Dauman’s “good reason’’ exit clause entitles him to almost $83 million, including stock considerations and benefits. He and Dooley have worked together since 1987.

While many top executives have contract terms that shield them from demotions or changes in control, it’s unusual for a senior executive like Dooley to be protected if another officer, in this case his boss, is let go. Both Dauman and CBS’s Moonves had terms in their contracts that allowed them to leave if they weren’t promoted to chairman of their respective companies when Redstone stepped down earlier this year.

If Moonves, 66, were fired or left with good reason, he would receive about $150 million, as well as offices, a personal secretary and insurance, company filings show.

Chief operating officer Joe Ianniello would receive about $50 million.

Dooley, 59, has been a Viacom executive for more than three decades. He joined a predecessor of the current Viacom in 1980. Redstone’s National Amusements acquired Viacom two years after that.

Dooley climbed the ranks, serving on the board from 1996 to 2000 before leaving to run a private equity firm with Dauman. They rejoined Redstone in 2006, Dauman as CEO and Dooley as chief administrative officer. Dooley became COO in 2010.

Over two years, the shares have lost half their value. Redstone is griping about the decline and objecting to the proposed sale of a stake in Paramount Pictures. He hasn’t singled out Dooley for criticism, and it’s possible he could choose him for the top job.

Material from The New York Times was used in this report.