The question here is really "Do they have the resources to move to where the work is?" Immigration to work better and earn more, whether temporarily or permanently, has been happening since transportation became a thing. Go to Dubai and see how many Pakistanis are doing jobs there. Or look in the average American commercial kitchen and count the Mexican and other latino immigrants.

Almost everyone in America is a descendant of immigrants, for that matter. In many cases, those immigrants were fleeing violence and persecution, their passage paid by overlords who felt it was very decent and moral of them to ship the people overseas rather than just killing them off (i.e. the Irish in America).