Yet as Mike Duggan, the mayor of the nation's largest bankrupt city, pledges to stem the flood of departures that have crippled Detroit and to begin increasing the city's population for the first time in decades, Mr. Ford is on the verge of losing his family's house. So are tens of thousands of others here who failed to pay their property taxes.

In a city that desperately needs to hold onto residents, there is a virtual pipeline out. At least 70,000 foreclosures have taken place since 2009 because of delinquent property taxes. And more than 43,000 properties — more than one in 10 in this city — were subject to foreclosure this year, some of them headed for a public auction where prices can start as low as $500.