DEIR AL-ZOUR PROVINCE, SYRIA (NYTIMES) - The men who emerge from the Islamic State in Iraq and Syria's (ISIS) last sliver of land are ordered to sit behind one of two orange lines spray-painted on the rocky desert floor: Syrians behind one and Iraqis behind the other.

The women, wearing face-covering veils and clutching toddlers, huddle in a different spot, also separated by nationality.

Several of the escapees are so badly wounded from incoming fire that they have to be carried to this open vista on mattresses to surrender to the US-backed coalition.

By midmorning, US Special Forces arrive in a convoy of armoured vehicles. The men suspected of being ISIS fighters are ordered to approach in single file, their arms outstretched, as they are searched by troops and a sniffer dog. Then they are fingerprinted, photographed and interviewed.

In the last two weeks, thousands of people have been streaming out of the village of Baghuz, the last speck of land under ISIS control in Iraq and Syria, an area where the group once ruled a dominion the size of Britain.

That state is all but gone. In the last month, the group went from holding three villages to two to just one.

The militants are now trapped in an area about the size of Central Park.

To the west, they are hemmed in by Syrian government forces. To the south is the Iraqi border, where Iraqi troops are holding the line. From the north and east, they are being fought by a US-backed Kurdish and Arab militia known as the Syrian Democratic Forces.

As the noose has tightened, even those who joined the caliphate in its earliest days are trying to save themselves.

Most of those who have made it to this spot in the desert in recent days are the families of the militants - their multiple wives and numerous children - with only a small number of locals originally from the area mixed in, Kurdish officials said.

Out of food, the families say they have been reduced to boiling a weed that grows in highway medians.

Large numbers of the escapees are foreigners, especially Iraqis who lived under the ISIS before fleeing to this corner of south-eastern Syria when Iraq's cities were liberated. But among the escapees who arrived in the last week are also Germans, French, Britons, Swedes and Russians, a testament to the group's broad appeal, which lured some 40,000 recruits from 100 countries to its nascent state.

On Sunday, US forces walked between the new arrivals with a hand-held screen, asking questions. Those who had government-issued IDs were told to hand them over. Their documents were placed in plastic pouches and hung with lanyards around the necks of the detainees.

They were sorted by sex and nationality, with foreign men presumed to be ISIS members, and loaded onto buses.

Some of the suspected fighters were taken to prison. The majority, including all the women and children, were told they would be bused to one of several detention camps in northern Syria.

After a lightning advance last month, the military operation to take Baghuz has stalled as commanders negotiate an end to the siege with the Islamic State, according to three US officials and two militia commanders.

Journalists taken Saturday to the front, the so-called zero line, marked by a berm about 300 yards from the first Islamic State position, found soldiers drinking tea and watching videos. Gun positions were unmanned, as if a cease-fire were in effect.

At stake in the negotiations is the fate of several dozen of the militia's troops who were captured by the Islamic State during a counteroffensive last fall. The group released a video showing one of the militiamen being beheaded.

Mustafa Bali, a spokesman for the Syrian Democratic Forces, said Islamic State representatives had asked for safe passage but that the request was rejected.

"We will fight every last one," he said.

But US officials said that safe passage to the Syrian province of Idlib was still on the table, and a militia commander said the group was asking for a truck of food.

The officials spoke on the condition of anonymity to discuss sensitive details.

Negotiating with the ISIS is controversial, but it has happened at numerous points throughout the now more than four-year-old battle to dislodge the group from the territory it once held in Iraq and Syria. According to local security forces, the deals, including prisoner exchanges, have saved civilians and infrastructure from a destructive bombing campaign.

While Baghuz is the last vestige of the Islamic State's caliphate in the region where it was born, the caliphate was always a global project, with 16 of its 35 "provinces" outside Iraq and Syria. Several of those overseas affiliates are flourishing, including in the Philippines and Nigeria.

Three reports issued last year estimated that the group still had between 20,000 and 30,000 fighters just in Iraq and Syria, where they continue to mount attacks.

One of the women who turned herself in Sunday was surrendering for the second time. The woman, Amal Mohammed al-Soussi, 22, arrived in the desert clutching the hands of her two toddlers.

She said that after her husband, an ISIS sniper, was killed during the battle for Raqqa in 2017, she surrendered to the militia and was held in a detention camp for eight months.

Then one day, she and dozens of other ISIS wives were loaded into trucks and driven into the desert, where they were handed back to the Islamic State. "They told us to get out and said, 'Now you are in your state,'" she said. "We understood that a prisoner exchange had occurred."

She said she had been a committed citizen of the caliphate, but that hunger had forced her to surrender. For weeks, she said, she and her daughters subsisted on animal feed. Another woman spoke of scavenging for a plant that grows in the crevices between houses and in traffic circles, which she boiled and forced herself to eat.

The increasing peril that the Islamic State's own families were subjected to was evident in the number of people who showed up every day with injuries.

One woman, her leg torn by shell fragments, was lifted from an arriving truck and held up as she hopped to the spot where other women were waiting to be screened. An older man collapsed on a mattress, suffering from a back injury. A woman in her 20s made it to the processing point, only to die soon after she arrived. Her family could do little beyond covering her with a blanket.

A schoolgirl from Turkey, the daughter of an ISIS family, was sitting wrapped in a blanket, unable to stand because of her injuries from a mortar round. And a six-year-old boy was rushed to a first aid station staffed by a group of recently arrived American aid workers.

"He's not going to make it. His pulse is too low," warned one of the paramedics, Jason Torlano of Yosemite, California, a member of an aid group called the Free Burma Rangers. The boy began trembling and whimpering in pain, straining from wounds to his head, arm and leg. The medics wrapped him in a heated blanket and tried to find a vein to start an IV drip, the bag of fluid taped to the hood of a Toyota Land Cruiser.

"Hey, buddy," the aid worker said, as the boy began to lose consciousness. "Stay with me." His mother stood nearby, repeatedly lifting the black fabric covering her face to wipe her eyes with a piece of Kleenex.

She said that she was from Aleppo and that her husband had been killed in an airstrike, but she denied being part of the Islamic State. Security forces from the Kurdish militia said they considered her and the majority of the others who have arrived to be the wives and children of ISIS members: Why else, they said, would a woman and a child who are not natives of the area make their way into an active war zone?

Using a stethoscope, the aid worker listened to the little boy's lungs. "He's drowning. We need to go," Torlano said, and bundled him into a car.

That afternoon, security forces dug a grave for the young woman at the edge of the rocky ground where the arrivals were being processed.

There was only one person there from her family, a cousin. He helped lower her body into the grave, uncovering her face just long enough to turn it toward Mecca.

The men digging her grave lifted their palms skyward in a five-second prayer.

Next to the freshly dug mound were three more, one of them just 3 feet long, the resting place of others who did not survive the caliphate.