Some fought in combat, but many did not. What followed were purposeless days, sleepless nights, and I sensed a bit of humiliation among them. Like Marlow on his way up the Congo, these men seemed to experience a disturbance in their Western consciousness. They had vastly overestimated their use. Their service was respected but insignificant. These were men who arrived with a stark idea of good versus evil, who thought of themselves as heroes, and found themselves turning in circles.

‘‘We perpetually give,’’ Harrington said. ‘‘And we are perpetually getting screwed.’’

In the months after the first volunteers arrived in the fall of 2014, the foreign fighters battled ISIS alongside the Y.P.G., but then they started dying. By the summer, at least six foreigners had been killed, including one American. The Kurds started using the foreigners for safer tasks — to secure remote outposts or cover guard shifts in rear areas.

Jordan Matson, a 29-year-old Wisconsin man who ran the Facebook page at first, was among the few who continued to join the most dangerous missions. He said he was the second foreign fighter to arrive. He had been in Syria’s Kurdish territory for almost a year and was the darling of the Western militia movement. He was so popular that one woman, writing on Facebook, threatened to kill herself if he didn’t marry her. Another, he said, tried to travel to Syria with her child to ask for his hand in marriage.

I met Matson while he was taking a break from sniper duty. We were in the basement of an apartment building in Tel Tamer, a ghost town with closed storefronts and dogs with cut-off ears. Matson was over six feet and had a big jaw, a goatee and a childish grin. He wore full fatigues and carried a Kalashnikov. I asked if he had time to talk. Yes, he said — he had nothing to do. ‘‘If I have no one to play chess with, then I’m going to stare at that wall,’’ he said. ‘‘And then I’m going to stare at that wall. And when I’m done staring at that wall, I’m going to stare at that wall.’’ Matson asked if I wanted any doughnuts or soda. He was going to get something from a man down the street who worked at the only operating store in town. ‘‘I have lots of money,’’ he said. He wouldn’t say where the money came from except a ‘‘generous benefactor.’’ Harrington told me the foreigners were given a monthly allowance of about $100 for their services from the Y.P.G., which they used for extra food and toilet paper.

Before the war, Matson had never been outside the United States. He was working the third shift at a meatpacking plant in Wisconsin. He joined the Army and served for a year and a half before being discharged. ‘‘Hey, we think you have PTSD,’’ he said his superiors told him. He added, ‘‘But I don’t.’’ He was going through a divorce at the time; he later decided he had an emptiness in his life because he hadn’t deployed.