DETROIT — Over the fierce protests of this city’s elected leaders, the State of Michigan plans to send an emergency manager to repair the deeply troubled finances of Detroit, one of the largest cities ever to reach such a dire point or to face such a level of oversight.

“There is probably no city that is more financially challenged in the entire United States,” Gov. Rick Snyder said on Friday as he explained why he had deemed Detroit’s woes too fundamental, too lasting and too large to be solved by the city itself.

Mr. Snyder’s call for an emergency manager, who would wield sweeping powers to reshape the city, underscored a long, troubling arc for Detroit. Once the cradle of the American auto industry and the nation’s fourth most populous city, it is now less than half the size it was decades ago and has a public sector plagued by more than $14 billion in long-term liabilities and annual worries of cash shortfalls.