New York makes an unusual promise to its residents: Its constitution says the state must provide “aid, care and support for the needy.”

But for at least the fourth time in almost 40 years, the state is being sued for failing to live up to this commitment by putting impoverished families at risk of homelessness.

A new lawsuit filed last month argues New York is failing for the same reason it has in the past: The welfare allowance it provides for housing, known as a shelter allowance, doesn’t come close to the cost of the state’s rents, which are among the highest in the country. The Legal Aid Society and Empire Justice Center, both nonprofits, are demanding that the state increase the allowance and provide enough financial assistance to keep families and individuals housed.

“I don’t want to sleep in the street. I don’t want to go to the shelter,” said 54-year-old Minerva Pacumio, a plaintiff in the lawsuit who is facing eviction. “I don’t want to lose everything.”

New York’s shelter allowance doesn’t cover rent for modest private housing anywhere in the state, according to the lawsuit and an independent analysis performed by New York Focus and ProPublica. The state hasn’t raised the monthly allowance for families with children since 2003 — when it was set at $450 for a family of four in New York City. And the amount has barely budged for adult-only households since 1988.

Pacumio receives a $250 monthly allowance to cover the one-bedroom apartment she rents in Queens for $1,900. She lives with her two adult daughters, one of whom is disabled; Pacumio handles her care herself five days out of the week. The other, Pacumio said, has mental health issues and has been unable to find work.

Pacumio said she owes thousands in back rent.

“When you don’t change your shelter allowance amounts for 40 years for single people and 20 years for families, I think........

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