Some states, including Florida and Missouri, have decided to shrink the duration of state unemployment benefits paid to laid-off workers, while others, including Arizona and California, are creating new restrictions on cash aid for low-income residents.

Here in Michigan, more than 11,000 families received letters last week notifying them that in October they will lose the cash assistance they have been provided for years. Next year, people who lose their jobs here will receive fewer weeks of state unemployment benefits, and those making little enough to qualify for the state’s earned income tax credit will see a far smaller benefit from it.

Some political leaders see these sorts of cuts as unfortunate necessities to help bridge their state’s financial gaps. Others see them as overdue limits on out-of-control government handouts — some lawmakers here fumed, for example, that 30,000 college students, newly dropped from the state’s food stamp rolls, should never have been allowed to collect such benefits in the first place.

Whatever the motive, such policy changes come as the downturn has left a growing number of low-income families in worse financial trouble.

The percentage of children living in poverty rose during the last decade, particularly once the recession hit and unemployment soared.

By 2009, about 2.4 million more children’s families lived below the poverty line than in 2000, an increase of 18 percent, according to a recent analysis of Census Bureau data by the Annie E. Casey Foundation, a child advocacy group. In states like this, where Republicans took control of the capital this year, the new cuts have helped resolve Michigan’s expected budget gap, once estimated at $1.4 billion.

“Michigan can no longer afford to provide lifetime assistance,” said Sheryl Thompson, an official with the state Department of Human Services, which reported that of those being dropped from the state’s cash-assistance rolls, some 1,200 families had been receiving payments for 10 years, more than 700 others for a dozen years, and an additional 400 families had been getting payments for 14 years.

The pattern of new cuts around the nation leads some advocates to fear that the number of low-income families will only grow in the next few years if programs they can lean on shrink or vanish.

“We’re O.K. unless something — anything at all — goes wrong,” said Rachel Haifley, who lives here in Lansing and said she works part-time making a little less than $9 an hour and receives child support for her two young sons, 1 and 3.

Ms. Haifley said she has become an expert at seeking out giveaways, thrift shops and bargains — for clothes, portable cribs, toys for the boys. “All I want is for them to feel like everyone else,” she said. “I don’t want them to grow up and ask me why they’re poor.”

In Dearborn Heights, Celia Kane-Fecay, another mother of two, said she has given up on the job hunt for now and returned to college — with help from $597 a month in cash assistance, Medicaid and any other aid she can track down with what she has come to describe unhappily as her daily list of begging phone calls. “You don’t ever want to be here,” she said.

Signs of new poverty are already evident. A project by the Annie E. Casey Foundation Kids Count Data Book found that by 2010, nearly 11 percent of the nation’s children, or 7.8 million children, had at least one parent who was unemployed, when only about half as many were in such circumstances in 2007. And since four years ago, the study found, at least 5.3 million children have been affected by home foreclosures.

Meanwhile, around the nation, lawmakers have weighed new limits to tax credits for low-income people; in Michigan, a proposal to throw out the earned income tax credit entirely was dropped, but lawmakers shrank the benefit — to an average of $138 a year for a Michigan family, advocates say, from $432 last year.

Six states have approved reductions in the length of state unemployment benefits. The notion appalls people like Jeananne Bishop, who has been desperately searching for a job since July 2010 and found herself washing her hair with laundry detergent at one point because she could not afford shampoo.

Ms. Bishop said her continuing benefits — now part of a federally financed extension — are the only thing keeping her afloat. Michigan’s shortened unemployment benefit limits will apply starting next year, but Ms. Bishop, 56, of Benton Harbor, seemed skeptical that much will have changed in the job market for them, cautioning, “No one calls back.”

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