I say this because I have heard way to many stories about this. It is unfair for us Americans. It is also selfish! Sure they are working for their family. But they do not ever care about the Americans whose jobs they stole! So yes they are stealing our jobs.
Internal Displacement of Citizens is a real issue. I have myself had my identity stolen by an immigrant woman from a wealthy oil family from India with an expired H1B Visa and she used my SSN to work. It has cost me a lot of money and grief and I was unable to get a job the year an immigrant took my name and identity to get a job and also went to college on my ID. I might have to change my name, and I still cannot file my return. The immigrant reported nearly 100k in earnings and my actual income has never been over 15k a year for myself. I am cleaning up a mess because not only did she steal an American job, she stole education credits, my HOPE tax one per person per life use credit, and she stole my name.
Although there is a pervasive belief that illegal immigrants are "stealing" American jobs, the fact of the matter is that illegal immigrants lack the paperwork necessary to land high paying jobs. As a result, many of them end up taking low paying migrant work, factory jobs, and under-the-table paying domestic positions that most Americans consider beneath them.