Are green card holders required to work?

7 hispanic adults are renting a house across the street from me. Two of them are women who appear to be stay at home moms. I know the owner of the house, a green card holder himself, rented the house to his concrete workers. They are part of his family also. It doesn't matter to me either way, but are green card holders required to work? One of the non-employed women has 5 children and she is pregnant with another. They are all considered legal US citizens now. What if the parents were sent back to Mexico? What would happen to their young children?