Some investors feared that China Evergrande Group , the world’s most indebted real-estate firm, would collapse spectacularly, triggering losses far and wide. Instead, the Chinese state is dismantling the giant developer slowly and behind the scenes, in what amounts to one of the biggest financial challenges Beijing has faced in years.

The plan, according to people familiar with the matter and official government statements, is to manage a controlled implosion by selling off some Evergrande assets to Chinese companies while limiting damage to home buyers and businesses involved in its projects.