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.

If Central Falls, a city of about 19,000, is able to reduce the benefits its retirees now get — something they will fight — it would not only unsettle the millions of public workers and retirees across the country, but also reshape the compact between governments and their workers. Most public workers now pay a portion of their salaries toward their pensions, but they may balk if they see those pensions can be cut when they retire. And governments that, like Central Falls, have not enrolled all their workers in Social Security as a money-saving measure may have to rethink that strategy.

Millions of teachers, police officers, firefighters and other government workers have long believed that their pensions were untouchable, thanks to provisions in state laws and constitutions. But some of those promises are unclear or untested, said Amy B. Monahan, an associate professor at the University of Minnesota law school who has studied the myriad laws protecting public pensions in different states.

Just how those promises would stack up against promises made to others, like bondholders, is unclear. It is also unclear how those state laws would hold up in federal bankruptcy court, which has its own ranking of creditors.

“This will all be up to a court to decide,” Professor Monahan said.

But many cities and states have already signaled that their bondholders take priority.

When Jefferson County, Ala., was poised on the brink of bankruptcy this summer after defaulting on more than $3 billion of bonds to finance a new sewer system, the state moved to help. Alabama’s new governor, Robert Bentley, proposed a plan to replace the defaulted bonds with new ones issued with state backing, which could lower the borrowing cost and avert what would otherwise be the biggest municipal bankruptcy in American history. Bondholders would forgive some of the debt they are owed.

Mr. Bentley’s move contrasted with the lack of action by his predecessor two years ago when the city of Prichard’s pension fund ran out of money and it simply stopped sending retirees their checks. Despite a state law saying that the pensions must be paid, no one in state government moved to enforce the law or propose a rescue plan.

“I’m a little ticked about it,” said Mary Berg, 62, a retired assistant city clerk from Prichard, who said she had sent news accounts of the proposal to help Jefferson County to local officials, asking why the state had never helped her and her fellow retirees. “The state didn’t even look at Prichard.”

Teachers in New Jersey likewise got a cold shoulder when they tried to make the state comply with a law that it contribute a required amount to their pension fund each year. A judge ruled that their plan was not yet unsound, despite the state’s failures to make the payments. The teachers, who argued that by the time the plan qualified as “unsound” it would have collapsed, lost on appeal last year. But the state always sets aside enough money to pay bondholders.

Illinois has some of the strongest bondholder protections anywhere, which explains how a state that began its fiscal year with $3.8 billion in unpaid bills from last year — and whose pension system has less than half of the money it needs — is able to keeping selling bonds.

State law requires Illinois to make “an irrevocable and continuing appropriation” of tax revenues into a special fund every month that can be used only to pay bondholders. Illinois’s pension system claims to have a “continuous appropriation” too, but it does not have meaningful deadlines and has proved much more porous over the years.

The federal bankruptcy code says pensioners and general-obligation bondholders are both unsecured creditors, stuck at the back of the line and treated as equals. But there is maneuvering room in the welter of state and federal laws. After Vallejo, Calif., declared bankruptcy three years ago, it cut payments to bondholders, but let workers bear their loss in lower pay and skimpier retiree health benefits. Pensions were untouched.

In Central Falls, the pension plan for the police and firefighters is projected to run out of money in October. But officials there say short-changing the bondholders will not bring relief. The next time the city needs to borrow money, investors will simply demand more in interest, and they might decide all Rhode Islanders were a bad risk and charge all cities more.

“The last thing we want to do is increase borrowing costs for all our cities and towns, and therefore cause tax rates to go up across the state, because one city has fiscal problems,” said Robert G. Flanders Jr., the state-appointed receiver for Central Falls, explaining the new state law putting bondholders first in line.

After going 20 months without their pension checks, the 141 retirees of Prichard decided a third of a loaf was better than nothing and settled with the city. Their average benefit, which had been $1,000 a month, is now about $350. But they also get Social Security. Ms. Berg, the retired clerk, said she worried about the retirees of Central Falls, many of whom do not.

“I can’t imagine telling them that they have to take this 50 percent cut,” she said. “These are retirees, elderly people. They can’t go out and get new jobs.”

Katie Zezima contributed reporting from Central Falls, R.I.

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