So, is the city bankrupt or not? Are creditors taking a haircut?
The city is bankrupt. The creditors are probably going to take a haircut.
When you say that in the UK, "the central government would step in", what do you mean, exactly?
Would the central government undertake to pay off the city's systemic budget shortfall in perpetuity?
Would it pay off the city's budget shortfall one time only, and compel the city to rationalize its budget to prevent further shortfalls?
Would it put the city into bankruptcy, pay off all the creditors in full, and then compel the city to fix its finances?
Or would it do something else that I haven't imagined?
I mean, I can see how maybe in the UK, being a relatively small, relatively densely-populated island, where everything has been tightly interconnected for centuries, and trouble in Sheffield or Liverpool may require swift and intrusive action from the central government to prevent the entire system from crashing down, such a thing as a city declaring bankruptcy might seem amazing.
In the US, such issues are usually left to the regional government. In this case the state government of Michigan, which has actually been involved in managing Detroit's deepening crisis for some time now.
One thing to be aware of is that the government of Detroit has actually
resisted the intrusion of the "central government" into its affairs. Instead, they have insisted on trying to manage their budget systemic budget shortfalls on their own. It's not for lack of trying that the state government didn't step in until recently.
At the end of the day, the city still owes debts it can't pay. The true law of the jungle would be a creditor free-for-all, with each one stripping the city of as much value as they could get their hands on, and devil take the hindmost.
Bankruptcy law is actually a much more civilized and moderate solution. You may want to consider
not putting much stock in sensationalized accounts of foreign countries.