But resources are scarcer than they once were. The Egyptian government has seized many of the exiles’ businesses and savings, while most struggle to find lucrative work in Turkey, said Ahmed Gad, a former lawmaker from the Brotherhood’s political wing.

“It’s hard to find job opportunities,” said Mr. Gad, hinting that their lives are subsidized by Turkish and Qatari institutions or their surrogates, and by wealthy members of the wider Brotherhood movement. “The same governments that are supporting our freedoms are supporting our lives here,” he said without further explanation.

Perhaps the Brotherhood’s biggest problem, however, is a lack of unity. Once a strictly hierarchical institution, members of the group now openly disagree about how it should respond to the current Egyptian dictatorship; how it should structure itself, should a political opening ever emerge in Egypt; and what it did wrong during its year in power from 2012 to 2013.

The group is now loosely divided between those who back the old hierarchy’s gradualist approach and a smaller faction that favors greater confrontation with the Egyptian state. “If revolutionaries take to the street, they should be able to protect themselves,” said Mr. Shalash, who is a leading figure in the second faction. “Not to initiate aggression,” he added. “Just to protect themselves.”

Then there are exiled Brotherhood members who support neither of the above, people like Abdallah Karyouni, a 31-year-old physician who finds both approaches unrealistic. The first group is “still waiting for Allah to make them victorious without mastering the political tools that will make them victorious,” Mr. Karyouni said. The second group “might lead the country to similar experiences to Syria and Algeria,” a reference to those countries’ civil wars.

During previous crackdowns, Brotherhood members and their affiliates have also spent time in exile, and the location of that exile has often affected their political approach upon their return home. “Just as where you study abroad in your 20s is important, where you spend your exile is also very important,” said Monica Marks, an academic at Oxford University who researches the Muslim Brotherhood and its offshoots.

It remains to be seen what lessons, if any, Egyptian Muslim Brothers will learn from living in Turkey. Brotherhood members disagree about whether the group should have tried to work with a wider coalition during its unhappy year in power or showed even greater strength.