A flier posted in one shelter last week warned residents in bold, underlined type, “Failure to make the required contributions could result in the loss of your family’s temporary housing.”

But advocates for the homeless said the new policy was punitive and counterproductive, and some shelter residents, in protest, have already refused to sign the documents acknowledging receipt of the rent notifications.

“Families have been told to pay up or get out,” said Steven Banks, the attorney in chief for the Legal Aid Society. “The policy is poorly conceived, but even more alarmingly, it’s being poorly executed. What is happening is that we have seen cases of families being unilaterally told, without any notice of how the rent was calculated, that they must pay certain amounts of rent or leave the shelter. We’ve already had a case of a survivor of domestic violence who was actually locked out of her room.”

Mr. Hess acknowledged that if a family does not pay the required rent, it could be told to leave the shelter, but he noted that residents can contest the rent required through a state hearing.

Ms. Dacosta, for one, said she had spoken with her caseworker and demanded a hearing. Martha Gonzalez, who is 49 and lives with her 19-year-old son in a rundown shelter in Fort Greene, Brooklyn, said she was informed last week that she owes $1,099 in monthly rent on a $1,700 monthly income as a security guard in Midtown. She said she planned to contest the rent demand in court.

City officials did not immediately respond to Ms. Gonzalez’s assertion that her rent would exceed half of her income.

Patrick Markee, the senior policy analyst of the Coalition for the Homeless, called the policy “impractical,” arguing that most working people who live in homeless shelters earn low wages and would be better off saving for a place of their own. “It’s going to make families stay in shelter longer because they’ll have fewer financial resources,” he said.

“They are taking money from them that could otherwise be used to help themselves get out of the shelter system,” agreed Arnold S. Cohen, the president and chief executive of the Partnership for the Homeless. “We’re dealing with the poorest people, the people who are the most in need, and we’re asking them to pay for a shelter of last resort. As a city and a state that has a history of social and economic justice, I think we can do better than that.”