Mohammed does not recall how the fight started but he can remember how it ended: with a police bullet in his knee. A fight had broken out in the Amsterdam squat where the 34-year-old Ethiopian lived along with 60 other asylum seekers from a roll-call of failed African states.

Four Somalis attacked him, says Mohammed. Normally, police leave the residents of the Vluchttoren, an abandoned office block known as the Refugee Tower, alone. But someone said they had seen a knife. The police arrived, a shot was fired and Mohammed now walks with a limp.

The episode was an extreme example of what life can be like in the six-storey block in the western part of the Dutch capital, which is home to dozens of failed asylum seekers who have fallen through the cracks of the EU asylum system.

Asylum applications are at a peak as people flee from war-torn countries such as Syria, leaving Europe facing its worse refugee crisis since the collapse of Yugoslavia. In total, 626,000 people applied for asylum in the EU in 2014 — a jump of 45 per cent from the previous year. Mohammed was one of the roughly 200,000 asylum applications that are refused every year. Dutch authorities did not believe his story, which entailed deportation from Ethiopia to Eritrea, escape to Yemen and then a journey to Europe, via Syria and Turkey. He has no legal right to remain. But, without proper travel documents, he cannot be deported. Instead, he lives in a legal no man’s land: unable to work or claim any form of benefit but unable to leave. The residents of the Vluchttoren rely on charities and their own wits to get food.

“Everything is paper,” says Mohammed. “If you do not have paper, you are nothing.”

Many EU governments seek to avoid the long-winded, expensive process of deportation, according to Elizabeth Collett, a director at the Migration Policy Institute Europe. “Laissez-faire is sometimes seen as the best option, especially if officials know they would be sending someone back to a dangerous place,” says Ms Collett.

Any attempt to head to another country within the EU should result in swift transfer back to the Netherlands, according to EU rules. Mohammed found this out the hard way, when he smuggled himself and his wife into the UK in the back of a lorry. When British officials realised Mohammed had already applied for asylum in the Netherlands, the UK’s Home Office sent him back over the North Sea.

Mohammed was one of 76,000 people that EU governments requested to send to other member states in 2013. The system is supposed to divvy up asylum claims efficiently, making sure that people claim refuge in only one country. But of these 76,000 requests, only 56,000 were accepted. Of these, just 16,000 actually resulted in transfers — Mohammed was one of the few. After two months Mohammed and his wife were flown back to the Netherlands. Two years later, he is still there.

Teklay, a 33-year-old from Eritrea, is in the same position. His asylum claim in the Netherlands was rejected in 2013. Eighteen months later, he lives in the Vluchttoren, sharing a small former office with two other Eritreans.

They sleep on single mattresses on the floor, with pictures of the Virgin Mary above their beds. Like Mohammed, Teklay is in the Netherlands illegally. When his asylum application failed, the Dutch government told him to leave. But without travel documents, there are few ways to exit and nowhere to go.

After escaping from Eritrea as a teenager, Teklay spent 14 years in Sudan before paying $1,200 to be transported across the Sahara in 2013. In Libya, he waited for nearly six months before embarking on a five-day crossing that ended on the shores of Sicily. Italian authorities separated women and children, as well as the sick. Fit, young men were left to their own devices. “To us, they said: ‘you can go’,” says Teklay.

Teklay’s experience is common. More than 170,000 people arrived in Italy in 2014 after crossing the Mediterranean, according to Frontex, the EU’s border agency. Yet, that year, Italy registered only 64,000 asylum applications, suggesting that the bulk of arrivals would crop up elsewhere. Teklay hoped to go to Sweden. Instead, he ended up in a place he had never heard of — Amsterdam. In bigger cities such as London, there is scope to find low-paid, illegal employment. But Amsterdam is small and there is little room for a black-market economy to develop. “If you don’t have documents, you do not have a life,” says Teklay. “You have no eyes, no mouth, no foot. It closes everything. Paper is life in this country.”

Teklay is hopeful that a DNA test from his mother will prove his Eritrean heritage and be enough for Dutch authorities to reconsider his application. Mohammed, meanwhile, has his hopes pinned on Canada, where an aunt lives. Beside the bullet-hole, there has been no ramifications from his fight this month, says Mohammed, who has patched things up with the Somalis. “There is peace,” he says.