Originally from Canada, Mr. Trebek became an American institution — and, then, in 1997, a U.S. citizen. He and the show both seemed so impervious to age that viewers reacted with shock to any mild change, such as when Mr. Trebek shaved his mustache.

And larger modifications, such as when the show revoked a work-week-long limit on how many times a winner could return to compete in the next day’s contest, proved contentious.

“I call it term limits,” said Richard Cordray, a five-time champion in the 1980s who went on to become the first director of the Consumer Financial Protection Bureau. “We always were annoyed. All of us who won five times thought we would go on forever.”

That small gripe aside, Mr. Cordray spoke admiringly of Mr. Trebek’s star quality, remarking on the way it propelled the show for so long: “Obviously he’s someone that people have really liked having in their living room for the last 35 years. It’s true of certain newscasters, it’s true of a few others — it’s a difficult quality to put your finger on but when somebody has it, it’s very apparent and he has it.”

Fans expected Mr. Trebek to go on forever as well, though Mr. Trebek has suffered several health scares in the past dozen years, including two heart attacks and a fall in 2017 that required him to undergo brain surgery.

“He just seems sort of immortal,” the journalist Jeffrey Toobin said in an interview. “I don’t think of him as having aged much.”