CENTRAL FALLS, R.I. — The retirees came from near and far, gathering in a muggy auditorium here to listen to an urgent pitch: give back a big chunk of your pension or risk losing it all.

This city of 19,000 is broke and headed for bankruptcy, partly because it has promised retired police and firefighters millions of dollars in pensions and benefits that it cannot begin to afford.

And so Robert G. Flanders Jr., a state-appointed receiver who is trying to right the city’s finances, found himself on the stage at Central Falls High School on Tuesday, asking retirees to help solve “a horrible dilemma” by giving up a significant part of what they had always assumed was untouchable income.

“No one blames any of you for this situation,” Mr. Flanders told the retirees, many of whom appeared well into their 70s and 80s. “We understand, believe me, that we are asking for great unanticipated sacrifices. But there is simply no money in the city to continue on the current path.”