David Ellison, a producer and billionaire financier of big-budget movies like “Terminator Genisys,” was on the verge of leaving Paramount for another studio home base; Mr. Gianopulos persuaded him to sign on with Paramount for four more years. That relationship has once again grown tense, however, with Paramount unhappy about Mr. Ellison’s decision to hire John Lasseter, who was forced to resign from Disney last year amid #MeToo allegations.

Mr. Gianopulos in November made a deal with Netflix to supply the streaming service with a handful of original movies a year, opening up a new revenue stream.

And Paramount finally has the full support of Viacom, where a new chief executive, Robert M. Bakish, has put into motion an aggressive turnaround plan. In an interview on the 52nd floor of Viacom’s Times Square headquarters, Mr. Bakish noted that he had just returned from Hollywood, where he met with agents, telling them that, unlike his predecessor, he has no plans to offload Paramount. If anything, Viacom was doubling down on the studio: We are open for business, so bring us your scripts.

“It was clear we had a major problem,” Mr. Bakish said. “But it’s Paramount — it’s the Mountain.”

Movie insiders want to believe that Paramount will respond to the heart paddles. But some people are privately sitting vigil.

When we reached Mr. Diller on a business trip in Europe to talk about his failed bid for Paramount and what has become of the studio and the movie business, his first reaction was to ask why anyone would bother writing about the studio.

“Why Paramount?” he asked. “It’s irrelevant.”