With most historians saying the Crusades stopped in 1291, and the disappearance of the Crusader States/Outremer, I'm left to wonder: what happened to the Europeans who had built a life there? Did they go back? Did they stay?
It appears that the crusaders were eventually pushed back onto Cyprus, which continued to have Frankish rulers for another three centuries.
Quoted from "The Civilization of the Middle Ages" by Norman F. Cantor:
"Indeed, Acre never fell to the Moslems. In 1291 the French knights who garrisoned it decided that their homeland had forgotten them and that the siege of many years to which they had been subjected would never be relieved. They arranged with the Arab general to surrender the castle and left with their honor intact and their crucifix-laden pennants flying high."
A large portion of the (ex-)Crusaders married local Christian women and stayed behind in the Levant after the demise of the Crusader states. The largest Christian community in present-day Palestine are the Latin-rite Catholics, generally believed to be descendants of Crusaders, though now they speak Arabic and are integrated in Palestinian society.
First, it should be noted that there were a lot of Eastern Christians in the Middle East before during and after the Crusades. Some of their cultural descendents still live in Lebanon and Israel/Palestine and Iraq and Syria. There are many Christians in Egypt.
If you're talking about Western colonists and their descendents, they almost certainly were all expelled by the Mameluke rulers of Egypt in the late 13th century. The famous general and Sultan Baybars did his best to erase all traces of Christian domination and he was followed by other Mamelukes who had the same policy. Experts on the Crusades basically think that Muslim rulers of Egypt and the Levant got tired of repeated invasions and did their best to make it impossible for Western Christians to establish themselves on the coast.
Cyprus remained under the rule of a French dynasty for a longer time, but eventually they went too leaving behind the much longer established Greek Christians who are still there.