The reason why New York City hasn't fallen into the same abyss is that the city has a very diverse economic base, and most of the rich are still living in Manhattan. Meanwhile, if you look at Detroit, the city is completely destitute, while the surrounding suburbs are some of the most prosperous in the country.
During the 1970s, Felix Rohatyn (of Lazard Freres) saved NYC from having to declare bankruptcy.
“Rohatyn became widely known in the 1970s for successfully restructuring New York City’s debt and resolving the city’s fiscal crisis. While running the Municipal Assistance Corporation for the city of New York, Rohatyn continued his deal making at Lazard. Although he capped his take at the firm at 6%, Rohatyn continued to be the preeminent rainmaker at Lazard well into the 1990s, completing such deals as Sony’s acquisition of Columbia.” Quote from Wikipedia.
Note: the Federal Govt. bailed out NYC to the tune of $2.3 Billion.