Thousands of Islamic State prisoners of war from around the world are being detained by the Syrian Kurd forces whom Turkey plans to target.

WASHINGTON — President Trump’s sudden blessing of a Turkish military operation in northern Syria and his announcement of an American troop withdrawal from that region raised questions about the fate of thousands of Islamic State detainees that the Turks’ targets, American-backed Syrian Kurds, have been holding in makeshift wartime prisons.

Mr. Trump insisted that Turkey must assume responsibility for the captured ISIS fighters and their families. But it is far from clear what will happen to them, and a host of issues arose from Mr. Trump’s abrupt, if still murky, change in policy.

What is going on in northern Syria?
The situation is deeply complicated. For now, the Kurdish-led Syrian Democratic Forces control northern Syria. They have been the primary American ally inside Syria in the war against the Islamic State, carrying out the brunt of the ground-level fighting with support from American airstrikes and weapons. They operate prisons where ISIS members are detained.

The Kurds are menaced from the north by Turkey, which has been fighting separatist Kurds inside its borders for years and considers the Syrian Kurds to be terrorists, too. Meanwhile, President Bashar al-Assad of Syria, backed by Russia, controls the southern part of the country and wants to eventually retake it all, raising the possibility of a deal with the Kurds.

The presence of American troops has helped maintain a fragile peace. But the White House said that Mr. Trump has given a green light for a Turkish military operation into northern Syria, and Mr. Trump said on Twitter that it was time to pull out. “Turkey, Europe, Syria, Iran, Iraq, Russia and the Kurds will now have to figure the situation out,” he said, “and what they want to do with the captured ISIS fighters in their ‘neighborhood.’”

Who are the ISIS detainees?
The Syrian Democratic Forces operate an archipelago of ad hoc wartime detention sites for captive ISIS fighters, ranging from former schoolhouses in towns like Ainissa and Kobane to a former Syrian government prison at Hasaka.

The prisons hold about 11,000 men, of whom about 9,000 are locals — Syrians or Iraqis — and about 2,000 come from some 50 other nations whose home governments have been reluctant to repatriate them. They also operate camps for families displaced by the conflict that hold tens of thousands of people, many of them non-Syrian wives and children of Islamic State fighters.

“If Turkey attacks these Kurdish soldiers, there is a grave risk that the ISIS fighters they guard will escape and return to the battlefield,” a bipartisan group of lawmakers who recently visited the Middle East said in a joint statement on Monday.

Would a Turkish invasion reach the prisons?
This is one of many unknowns. An American-brokered plan in the works would create a demilitarized “safe zone” a few miles deep along a roughly 78-mile portion of the Syrian-Turkish border to reassure Turkey and forestall any military conflict with the Kurds. That would not affect the Kurds’ ability to keep running the prisons.

But Mr. Erdogan, speaking at the United Nations General Assembly last month, has instead pushed for a much longer and deeper zone. A broader invasion could reach the prisons, and it would set off an armed conflict that could prompt the Kurds to pull guards from prisons so they could instead join the fight.

The “worst-case scenario” is that the Kurds are so frustrated and angered by the United States’ action that “they decide to release wholesale some of the detainees,” said Christopher P. Costa, a former senior director for counterterrorism on Mr. Trump’s National Security Council who now heads the International Spy Museum.

Is Turkey planning to take custody of ISIS prisoners?
It was not clear. The White House said Turkey would “now be responsible for all ISIS fighters in the area captured over the past two years.” But Turkey has given no public sign that it has agreed to take over that headache.

For now at least, the Kurds have told American officials that they will continue to hold the ISIS detainees. But a senior State Department official acknowledged that the best-trained guards could be pulled away in the event of a conflict with Turkey, calling it a “big concern” that some ISIS fighters could go free.

“It’s hard to imagine Turkey has the capacity to handle securely and appropriately the detainees long held by the Syrian Kurds — and that’s if Turkey even genuinely intends to try,” said Joshua A. Geltzer, a former senior director for counterterrorism at the National Security Council in the Obama administration.

Why did Trump complain about Europeans?
The Kurds have implored countries around the world to take back their citizens who fought for the Islamic State and were captured. But that idea is politically unpopular in many European countries. Mr. Trump is correct that nations like Belgium, Britain, France and Germany have been largely content to let the Kurds bear the burden of detaining their citizens — particularly the male fighters.

Many European law enforcement officials fear that if they repatriate their extremist citizens, they would be unable to convict them or keep them locked up for a long time. European counterterrorism laws are weaker than those in the United States, where a conviction merely for joining a designated terrorist group can yield a 15-year prison sentence.

But Mr. Trump was wrong when he also said that the captured ISIS fighters were “mostly from Europe.” While scores of the imprisoned men have European citizenship, far more come from other countries that are part of the Muslim world — like Tunisia, Egypt and Yemen, to say nothing of the thousands of local Syrians and Iraqis.

What about the ‘Beatles’?
Unlike many other countries, the United States has taken its citizens off the Kurds’ hands. But there are two British detainees still in Kurdish custody whom the United States has a particular interest in keeping locked up: El Shafee Elsheikh and Alexanda Kotey.

They are two of the so-called Beatles, a four-member cell of British ISIS members who tortured and murdered Western hostages, including James Foley, the American journalist who was beheaded in August 2014 for an ISIS propaganda video. Another member of the cell, who was later killed in a drone strike, is believed to have killed Mr. Foley.

The Justice Department intends to eventually bring them to the Eastern District of Virginia for trial, but a court fight in Britain has delayed that transfer. The lawsuit is over whether the British government may share evidence with the United States without an assurance that American prosecutors will not seek the death penalty.“It’s a good day for the Beatles,” said Senator Lindsey Graham, a South Carolina Republican who is normally a staunch Trump ally but who denounced the president’s move as “complete chaos” and “a disaster.” In a phone interview, Mr. Graham vowed to lead a congressional vote to try to impose sanctions on Turkey if it invades northern Syria, despite Mr. Trump’s acquiescence.