After years of boom and rocketing prices, the prospect of a bust is looming over China's vast property sector, with authorities hoping to avoid a meltdown that could send shock waves through the world's second-biggest economy.

Housing was doled out by the state when Communist-style collectivism dominated economic management. But in the past two decades that has given way to market-oriented principles as China’s economy has opened. New home prices have soared, more than quadrupling in Beijing and Shanghai since 2003, and more than doubling in…