I guess I would annex the nearby suburbs, deliberately targeting the more affluent ones (Grosse Pointes, Ferndale, etc.) and use the subsequently increased tax revenue to buy up the abandoned buildings in the worst neighborhoods and replace them with livable housing. This would obviously have to move fairly slowly because there wouldn't be that much more revenue.
Obviously this would never happen.
That seem a very bad idea, as it only will result in people (with money) leaving those suburbs and leaving Detroit to administrate new collapsing neighbourhoods.
From what I have read about Detroit, the bad blood between the sururbs and the city are so ugly, that it would be a disaster to unite them, and would only result in people further away.
In fact my suggestion would be the other way around, Detroit should become smaller, cut off depopulated areas from Detroit, and offer the remaning population to relocate to other neighbourhood. This would lower the public expenses for Detroit and make it easier for police and fire departments.
Afterward I would offer the now empty areas to developers more or less for free. The result could be new sururbs closer to the city.