The reductions force some families to apply for welfare for the first time, while others become increasingly dependent on food stamps or risk eviction when they come up short on rent.

“In many cases, it’s devastating,” said C. A. Watts, the director of the district attorney’s family support division for Clark County. “Some of the parents absolutely depend on that money coming in. It’s a domino effect. The custodians need the money to feed and clothe the children. If the money stops, it puts a burden on the custodial parent, and they have to come up with funds another way. They’re not going to let their children starve.”

The amount of child support varies based on individual family circumstances, but New York State begins with these guidelines: A noncustodial parent generally pays 17 percent of gross income for one child, 25 percent for two children and up to 35 percent for five or more children, as well as a share of child care, medical and education expenses.

“We see everything,” said Peter Passidomo, chief of the state’s 125 support magistrates. “High income, low income, across the board. It’s just like in an intact family where the income earner has lost the job.”

Though Family Court in New York is open to the news media, names of the parties are typically not revealed.

Judge Troy, who has been a Family Court judge since 1999, said that in recent weeks he had seen a former Lehman Brothers executive whose $7 million in stock had disappeared, leaving him unable to pay his child support. And then there was the divorced couple whose combined income had surpassed $400,000  until they both lost their jobs and were scrambling to figure out how to pay two private-school tuitions on roughly $800 a week in unemployment benefits.

Most, though, are more like the man who went from a decent-paying factory job to working in food service during Mets games in Queens. Judge Troy lowered his monthly payment for his three teenagers to $50 per month, from $686. Otherwise, he feared, the father would be unable to meet his obligation and face a more drastic punishment: jail.