UIJEONGBU, South Korea—On Aug. 1, Chey Tae-won, one of South Korea’s richest and best-connected men, will celebrate a $7.6 billion merger that consolidates his control over SK Group, a sprawling conglomerate whose businesses include oil refining, chemicals, telecommunications and the world’s second-largest manufacturer of memory chips.

But there won’t be any champagne for Mr. Chey. The 54-year-old SK Group leader oversees his empire from a prison cell in this far-flung suburb of Seoul, issuing directives for his various companies...