Close them down ???? No! we need basic research!
Tell them they have to admit US citizens first. If no US citizens qualify that has to be put in writing with signature of the grad student coordinator, the department head & the dean attesting to the fact no US students fill the bill. If student’s home country is discovered using the IP developed at the university and paying no royalties back to the university. The university must refund the state & fedgov the cost of the student plus cost of the research.
Do that & the problem would soon resolve itself.