When Lee Kun-hee, the patriarch behind Samsung Electronics, died in 2020, his dynasty soon dealt with a crisis on two fronts: first, a multibillion-dollar inheritance tax. The following year, his son Jay Y. Lee was jailed after being convicted of bribing South Korea’s former president Park Geun-hye to win support for his succession.

At the time, some observers speculated that the sheer scale of one of the world’s largest death levies could threaten the family’s control over the...