One of those migrants, a mother who crossed the border with her children, spoke to Eyewitness News about what the family endured to make it to New York.
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Amlidey Alvarez of Venezuela made the journey last fall with a group of 56 people, 17 of them children. Photos and videos of their trek through the jungle in Panama were taken by other members of her group. Her phone was stolen in another harrowing part of the journey.
"We were held captive by the Juarez cartel in Mexico," said Alvarez, speaking originally in Spanish. "They left us without money, clothes or cell phones."
The group was kidnapped and told they were being detained for unauthorized travel.
"Armed people who are carrying three or four immense weapons, which your children can't see," Alvarez said. The children are "scared, they hug you, they tell you, 'Mama, what's happening?'
She'd tell the kids: "'Don't worry. Don't be nervous. Close your eyes, try to sleep.' That's how we had to manage the psychological aspect with the children, who did not understand what was happening."
The families kept their spirits up, but that ordeal left them with even less than what they started with.
So, when some of them got to New York, the weekly resource fair at Saint Paul and Andrew Methodist Church on the Upper West Side helped restore their faith in humanity.
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"It was all word of mouth so we would have 40, then the next week 80, and then 150, and now we're seeing between 200 and 300 families each week," Rev. K. Karpen of the church said.
Erica Depiero is with Manana Otro Dia, an organization that helps families like Alvarez's adjust as they send their kids to school.
"If we could let them do the asylum process, give them jobs, move them out of shelters, let them earn some money, they're going to be contributing to our society very quickly," Depiero said.
"They don't want a handout," Karpen said. "They want permission to work and that's really up to the federal government at this point to streamline some way, for people to work legally."
The new Title 8 requires migrants to prove another country has rejected their claim to seek asylum before they can enter in the United States.
"Suddenly, you arrive here with hope - because that's the word, hope and they suddenly shut it down on you," Alvarez said. "That's a blow, that's very painful because what we are simply asking for is an opportunity."
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As more migrants continue to arrive with that same hope, the city is also changing policy.
Officials recently suspended the nightly deadline for placing families in shelters and the requirement that families be placed in private rooms, not group settings.
New arrivals and families that have been here for weeks or months need shelter while they try to get on their feet as they wait for their asylum process.
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