“Bankruptcy scares me,” said LaTanya Boyce, a nurse practitioner. She urges her patients to treat health concerns before they become acute because, she said, “if they find themselves calling 911, it’s probably too late.”

But as with many here who have wrestled with the practical realities of living in this city, Ms. Boyce said she would not mind if some entity other than the city took over the management of Belle Isle, a park whose plan was conceived in the early 1880s by Frederick Law Olmsted. Ms. Boyce goes to the park for exercise, wearing a fanny pack that at times contains a gun — “Do you see any city police here?” — and bemoaning several locked restrooms that have portable toilets planted in front of them.

“I would love to see it leased to the state,” she said of the park. “They’d take better care.”

Recent developments among Detroit’s elected leaders have only added to the sense that significant changes in the city are perhaps even preferable. Two of the nine City Council members have resigned. (One said he was leaving to work for the emergency manager’s office.) Then, Charles Pugh, the Council president, had his salary stopped and power stripped by Mr. Orr after the councilman abruptly stopped showing up for meetings and disappeared from public view.

“Where Is Charles Pugh?” a headline at the top of the front page of The Detroit Free Press asked.

“For a lot of people, I think city government has become a nonentity here,” said Kurt Metzger, the director of Data Driven Detroit, which tracks demographic, economic and housing trends in the region. “People almost feel like the city goes on in spite of city government — that city government in this case certainly doesn’t define the city — and that affects how they’re feeling about what comes next.”

Recently, Mr. Orr indicated that Detroit was getting out of the business of electricity distribution. An independent authority is already planning to take control of the city’s streetlights, 40 percent of which, Mr. Orr’s office said, were not working in recent months. Similar handoffs are being weighed for the water and sewer services, and possibly more.