Brett Ludwig, a Tyco spokesman, said the company’s success “in large part results from key strategic decisions made by Mr. Breen and the Tyco board to create five new publicly held companies, each of which is a leader in its respective field,” adding that Mr. Breen’s pay “reflects the increase in value of Tyco’s shares.”

Other times, huge payouts go to executives as a result of takeovers. Douglas L. Foshee received millions after El Paso, the energy company he led, was taken over by Kinder Morgan.

Extreme exit packages for chief executives became more common during the hostile-takeover era of the 1980s, when the so-called golden parachute proliferated. Boards realized that without the promise of compensation, executives would be unwilling to negotiate deals to sell their companies if an outside takeover would force them into the unemployment line. Provisions were written into employment agreements that provided everything from lump-sum payments equivalent to several years’ worth of salary to extended health insurance benefits.

“They became larger in an era when executives were resistant to having companies sold and having new management come in and basically firing the C.E.O.,” said Mark Kennedy, an assistant professor at Imperial College Business School in London. “Nobody had any idea how big they would become.”

Professor Kennedy, a co-author of a paper about this practice with Peer C. Fiss of the University of Southern California and Gerald F. Davis of the University of Michigan, said that more than 60 percent of Fortune 500 companies had golden parachutes in place by 1990. Today, about 82 percent of the chiefs of Standard & Poor’s 500 companies are entitled to some type of cash payment if they are replaced upon a change in control, according to GMI Ratings, a corporate governance firm.

Amid public anger over ballooning compensation, such contracts often became more complex and opaque. And many companies disputed that current severance payouts or enhanced retirement packages are really “golden parachutes,” designed to offer soft landings in the event of takeovers. However they are characterized, hefty packages for departing executives are still common.

“The main reform that I would like to see is not have severance agreements that are soft landings for executives who did a poor job,” Professor Kennedy said.