This is difficult in most countries and extremely so in the US. Which benefits? How do they prove entitlement to them? By what process are they entitled to them but the military vets living on the street aren't?
I'm not saying it doesn't happen, but I suspect it happens a lot less often than you think.
(also, you've done the old "Schroedinger's immigrant" thing: at the top of the thread we were talking about jobs, you're talking about benefits now. Who are these people who simultaneously go on benefits while also stealing your job?)
At the same time their children, whether "dreamers" or native born get free education and healthcare the average cost per student in the US is around 15k the highest in the world, which these kids receive for free despite their parents never paying into the system.
The end result is that illegal immigration costs US federal and state governments 85-100 billion a year.
I support highly skilled labor ie top .1% of worldwide talent, not unlimited immigration sponsored by corporations to drive down wages for US citizens, whether that be low skilled manufacturing or software engineering
http://www.politifact.com/truth-o-meter/statements/2016/sep/...
https://fairus.org/issue/publications-resources/fiscal-burde...