As a result, suburban municipalities — once concerned with policing, putting out fires and repairing roads — are confronting a new set of issues, namely how to help poor residents without the array of social programs that cities have, and how to get those residents to services without public transportation. Many suburbs are facing these challenges with the tightest budgets in years.

“The whole political class is just getting the memo that Ozzie and Harriet don’t live here anymore,” said Edward Hill, dean of the Levin College of Urban Affairs at Cleveland State University.