At what sort of job that would make the initial investment worthwhile?
Working off the books can be profitable, even if the pay is lower than the norm for that kind of job. They can probably land such a job and a place to stay with some relative in the states, of which they have many. The reason is that while doing work off the books, they can also get fake IDs and start cashing in on charitable organizations' goodwill, both the typical charity oranizations we all know, and the Muslim ones we don't. They can add on a selection of welfare programs as well. They can also get free health care. And they can spend their time looking for some American citizen to marry.