Following a complaint of abuse or neglect, the CPS (Child Protection Services) worker is required to investigate immediately. If the abuse/neglect is substantiated, four future directions or choices present themselves.
I am unaware of any law that prohibits such a placement. Laws concerning immigration differ state by state. Obviously, the purpose of child protection laws is to have children placed with family first. However, there are several extra-legal questions that occur to me. Would the relative put himself/herself in jeopardy by coming forward? If deported, would the relative take the child with him or her? Check with a group in your state that is supportive of undocumented persons. Then ask yourself: What is best for the child? Good luck in making a hard decision.