Sony Pictures, which includes Columbia Pictures, TriStar Pictures, Sony Pictures Classics and other entities, also has reshuffled its executive ranks in recent months, shedding several veteran officers and hiring two key executives.
In August, Sony partnered with former Fox Filmed Entertainment Co-Chairman Tom Rothman to restart its TriStar Productions banner.
In December, the studio named producer Michael De Luca, whose credits include "Captain Phillips" and the forthcoming "Fifty Shades of Grey" adaptation, president of production for its Columbia Pictures unit.
Those hires helped fuel talk that Pascal, who has worked at Sony since 1996 and has a contract that expires in 2015, might become the next studio head to depart. Warner Bros. film head Jeff Robinov had stepped down in June, and Universal Pictures' Adam Fogelson was let go in September.
Lynton said he fully supports Pascal.
"In no uncertain terms, it never occurred to me to replace Amy," said Lynton, chairman of the studio and chief executive of Sony's entertainment arm, which includes the studio, Sony/ATV Music Publishing and Sony Music Entertainment.
"I think she is doing a terrific job in the role she is playing in the company," he said.
Added Rothman: "Amy is an exceptional, first-rank studio head and I can't imagine that she is going anywhere. I certainly hope not."
"Tom and Mike are fantastic hires," Rudin said. "But they are hires."
Loeb, whose hedge fund Third Point owns about 7% of Sony, said in a July letter to his company's investors that the company's entertainment arm was "poorly managed."
But a source with knowledge of Loeb's current thinking on Sony Pictures said the recent changes at the studio — from the budget cuts to a new emphasis on television production — have left the hedge fund investor "hopeful."
The business side of Hollywood always wants executives who can drive hard bargains.
Pascal's fans, however, say that it's her film smarts that make her so valuable to Sony.
Barbara Broccoli, who produces the James Bond films, said that Pascal was instrumental in rebooting the franchise, which took a darker turn with 2006's "Casino Royale." Pascal supported the controversial casting of Daniel Craig as 007 in that film, Broccoli said.
"It would be hard to find anyone other than Amy who would have … been so supportive with us," Broccoli said.
The most recent Bond picture, 2012's "Skyfall," grossed more than $1.1 billion worldwide. That film helped Sony Pictures finish No.1 in box-office market share in 2012, but it was fourth last year.
Despite the Golden Globe wins and a slew of Oscars over the years, Sony Pictures Entertainment has never released a film that won the Academy Award for best picture. This year, a handful of Sony's films could be nominated in that category.
A win would be massive. But even the nominations mean something, Rudin said.
"If they come out of Thursday with three of the 10 best picture nominations, that's an astonishing level of success — but all of them were in the works before there was a Daniel Loeb conversation," Rudin said.