Can post graduate students be forbidden to work in the institution they are studying?
No.

In North America, at least in science and engineering, PhD students are generally expected to work for their host universities as either teaching assistants or research assistants, except for the relative few who win full-ride fellowships.  This expectation is strong enough that it is considered foolish to accept an offer of admission to any PhD program without a simultaneous offer of a fellowship or assistantship.  Sometimes these assistantships are also available to Master's students.