Lee Jung-jae is everywhere in South Korea: on TV, in fashion shows, and on ads selling everything from insurance to instant noodles.

He was already an established leading man in South Korea when his star turn in Netflix’s hit series “Squid Game” elevated him further at home and brought him global attention. He became the first Korean to win an Emmy for acting and was the first Asian to be cast as a Jedi Master in the “Star Wars” franchise.

But superstardom in South Korea also means heavy scrutiny from fans, who can quickly morph into critics and harassers. Their backlash has roiled careers and, in a few extreme cases, culminated in celebrities dying by suicide.

“It is a burden,” Mr. Lee said of South Korean fans’ expectations, in a recent interview. Audiences here root for their favorite stars “with the heart of a family member.”

That, experts say, can make a letdown from a celebrity intensely personal for audiences in South Korea.