Can illegal immigrants get government assistance?

I don’t think they can but I could be wrong. Even so, would it be right, in your mind, so deny a child basic health care and food just because they weren’t born here or their parents came here illegally?
There is an assumption that illegals come here and they refuse to work, they’re lazy, they’re just living off the dole, but I don’t think that’s the case either.
What are your thoughts?