At the end of last year, New York stopped offering a sort of last-resort program known as extended benefits that lasted for up to 20 weeks. Now, the longest an unemployed New Yorker can collect benefits for is 79 weeks.

But some who only recently started collecting emergency benefits, like Ms. Cozart, may only collect them for a maximum of 37 weeks. For most of that period, the benefits would be reduced by the automatic cuts.

The $44 a week that Ms. Cozart will lose may not sound onerous in New York City, where it would barely cover one prix fixe dinner during Restaurant Week. But advocates for the unemployed point out that they had to lobby for years in Albany to obtain the $5 increase in weekly unemployment benefits that New Yorkers are scheduled to receive next year.

That increase, the first since 2000, will raise the maximum weekly benefit in the state to $410. But it still will be at least $180 lower than the maximum benefit in Connecticut or New Jersey.

Ms. Cozart’s last role was as Aunt Gert in an Off Broadway revival of “Lost in Yonkers,” and she had hoped to find another acting job. But with a baby to feed and clothe and a husband whose job does not provide health insurance, she said she had begun considering office jobs.

“I would much rather have a job that paid well and provided health benefits than be sort of scrimping and saving,” said Ms. Cozart, 42. Referring to the cut in her weekly benefits, she said: “$40 a week adds up. It just made me see red, made me really angry.”

For Patricia Torres, 29, the cut will just be the latest indignity that has followed the loss of her job selling wireless phone service in Downtown Brooklyn in June. Ms. Torres, who said she earned $60,000 a year before she was dismissed, said she had to move out of a Manhattan apartment she shared with a roommate and back in with her grandmother and ailing grandfather.