In practice debt restructuring and those providing the new/bridging loans (often the same banks that gave the old loans) putting down demands.

If the demands aren't accepted, loans aren't provided. If loans aren't provided, salaries won't be paid and city employees will be fired.

The demands will include cutting costs, defaulting on pension plans (and dealing with the legal consequences) and the like.

Since the city is in default, they won't have the same level of autonomy to accept or reject.

Capitalist takeover, basically.

Doesn't happen often though. You can find some accounts if you look for it. Detroit has gone through this recently, but there are other cities that dealt with issues like this in the past. New York had it at some point, though I think they narrowly avoided default by accepting the terms of the bankers.

Probably the terms of the bankers lead to modern new Yorks success.