When the small, beleaguered city of Central Falls, R.I., filed for bankruptcy this month, it sought to cut the pension checks it has been sending its retired police officers, firefighters and other workers by as much as half. All the city promises now is that its retirees, many of whom do not get Social Security, will not have their benefits cut to less than $10,000 a year.

But investors who bought the city’s bonds could do much better: Rhode Island recently passed a law intended to make sure that they would be paid in full, even in bankruptcy.

Retirees are wondering how the city can cut what they believed was a guaranteed benefit. “We put our time in, we put our money in,” said Walter Trembley, 74, a retired Central Falls police officer. “And the city, through their callousness and everything else, just blew it. They were supposed to put money in and they didn’t.”

Cities and local governments make lots of promises: to their citizens, workers, vendors and investors. But when the money starts to run out, as it has in Central Falls, some promises prove more binding than others. Bond lawyers have known for decades that it is possible, at least in theory, to put bondholders ahead of pensioners, but no one wanted to try it and risk a backlash on Election Day. Now the poor, taxed-out city of Central Falls is mounting a test case, which other struggling governments may follow if it succeeds.