Among the top accusations against Turkey during Syria’s ongoing civil war has been that its government has not done enough to stem the flow of foreigners who slip over its border and into the ruthless jihadi groups operating between Syria and Iraq. But just as those thousands have crossed the boundary into Syria and Iraq to take up arms — some are thought to have joined extremist factions like the al-Qaeda-linked Jabhat al-Nusra and the Islamic State of Iraq and Greater Syria (ISIS) — Turkey’s 560-mile-long border has also proven a valuable exit for more than 1 million Syrian refugees. Officials estimate more than 138,000 Syrian Kurds joined them in recent days, putting that exodus among the largest population shifts of the conflict since it began more than three years ago.