SEOUL, South Korea — On May 10, the chairman of the Samsung Group, Lee Kun-hee, had a heart attack and stopped breathing. He was resuscitated at the hospital but remained in a coma for more than two weeks. As the country waited for information about his condition, rumors ran rampant. One of the most widely circulated was that Mr. Lee, 72, had already died and Samsung was covering it up.

Samsung announced last week that Mr. Lee had stirred. One story goes that the chairman opened his eyes for a moment just when Lee Seung-Yeop, a Samsung Lions’ slugger, hit a home run.

The obsession with Mr. Lee’s condition speaks to Samsung’s outsized importance to the South Korean economy. Samsung is the prime example of a chaebol, one of the massive family-run conglomerates that are credited with leading the country through its postwar surge from an impoverished country to an economic powerhouse. Chaebols flourished with the support of successive authoritarian regimes, which lavished them with tax breaks and protection from foreign competition.

But many South Koreans feel that chaebols have become too powerful. Several high-profile corruption scandals in recent years involving chaebol executives, and the light treatment they received from the courts, have only deepened the sense that the corporate behemoths have become too dominant. But is South Korea ready for weakened chaebols? What would happen if a company like Samsung were to fail? That’s the question that naturally arose when Lee Kun-hee slipped into a coma.