Chairs and tables lined El Paso’s new Migrant Welcome Center in west Texas, where families who have crossed the US-Mexico border without immigration papers were meeting with volunteers and city employees, or making phone calls to loved ones elsewhere in the United States.

Children amused themselves in a designated play area, while their parents worked out where the next steps of their journey would take them and how they would get there.

Services on offer at the city-funded facility included food, water and basic healthcare, assistance with communication and travel arrangements – though not beds.

A 40-year beacon of refuge shuttered in the city earlier this year. The local non-profit Annunciation House, which works to help migrants arriving in the area, announced that it would be closing its largest shelter, Casa del Refugiado, due to maintenance issues and a lack of volunteers.

It had the capacity to house up to 1,500 migrants and had weathered years of turmoil in immigration policies, helping migrants in dire straits as they were put into federal detention or ended up on the streets.

Without that, the city’s new facility, which opened last month, has to find other shelters for those without alternative housing to go to, which are already bursting at the seams, or get them on their way to another city as fast as possible – including via controversial bussing practices.

The center can help up to 300 migrants at any given time. No one is housed there overnight so it cannot replace Casa del Refugiado, but is nevertheless a stark change from the chaos of a few weeks ago when city authorities set about breaking up what they called public camping, as migrants slept on the streets of downtown.

Customs and Border Protection in El Paso has been stretched by recent increases in border crossings and apprehensions and at one point in September almost 1,000 migrants were released to the streets of El Paso in a six-day period.

Bewildered, hundreds set up camp outside the local Greyhound bus station, some in donated tents, despite stormy weather and a lack of bathrooms and washing facilities, and the makeshift camp became squalid.

Asylum-seeking migrants walk out of the Rio Bravo river after crossing it to turn themselves in to US border patrol agents in El Paso, Texas, as seen from Ciudad Juárez, Mexico, last week.

When local media questioned the city on their response, information was not forthcoming and instead a statement was emailed, which said: “Staff is focused on the work regarding the migrants and is unable to conduct interviews at this time” and that the city was working on assistance and cleanup.

The next communication was an invitation for media to visit the newly established welcome center.

Many of those being assisted are asylum seekers who after crossing the border were given leave to stay in the US and fight their legal case. Many are from Venezuela and Nicaragua.

El Paso’s deputy city manager, Mario D’Agostino, said about 50% of the people don’t have the funds to travel onwards, whether they are meeting family or immigration sponsors elsewhere in the United States or are not due to meet anyone but want to find housing and wait for work papers while their cases go through the over-burdened legal system

El Paso has chartered nearly 40 buses to transport migrants to New York City.

Several Republican-led states, including Texas, Arizona and Florida, are participating in these latest moves to bus (and sometimes fly) migrants to larger and typically Democratic-run cities, including Chicago, New York and Washington DC, and beyond – but without prior agreement from or liaison with the authorities in those cities.

Dylan Corbett, executive director of advocacy group Hope Border Institute, decried the actions.

“What the governors of Texas, Arizona and Florida are doing is immoral and unethical,” he said.

The institute works on the ground in El Paso and its sister city across the Rio Grande in Mexico, Ciudad Juárez, but also in countries further south, such as Guatemala, providing aid to migrants.

In El Paso, some are taken to the airport where, if they can afford it, they are flown to relatives or sponsors in the US. Others wait in lines by the hundreds to board buses.

“The overwhelming number of individuals or families do not remain in El Paso. Almost 100% of them move on to other parts of the US,” said Ruben Garcia, director of Annunciation House.

But the waves of people fleeing chaos and oppression in Venezuela, in particular, don’t have anyone waiting to receive them in America.

“The assumption is that everybody, 99%, continues to move forward and what we’re seeing is that you got a significant population of people from Venezuela who don’t have sponsors,” Garcia said.

A surge of Venezuelan migrants combined with a loss of shelters in El Paso is creating a whirlwind.

“The exodus of Venezuelans from their country due to the political and economic situations there represents one of the largest migration crises in the world right now,” Corbett said.

Without Casa del Refugiado and in the absence of more state or federal support, local non-profits, including church groups, are banding together in the hopes of filling the gaps.

“Currently we are working with the diocese of El Paso on a major plan to expand the hospitality provided by the Catholic church in El Paso to meet the needs,” said Corbett.

He said the partnership was able to house around 700 migrants in a week.

The El Paso county commissioners court approved funds for a county-operated shelter to assist with travel for migrants. County judge Ricardo Samaniego said they were working on a second location, though neither will provide housing for migrants and that responsibility falls on the city.

Garcia had warned city officials before closing Annunciation House’s largest shelter that people would end up on the streets if there was a surge in border crossings.

In an interview on ABC’s This Week, El Paso’s mayor, Oscar Leeser, said that border patrol agents encountered nearly 2,000 migrants on one day the previous week, but noted in recent day that no one has been simply turned out into the street nor had there been a return to public camps.