Well, generally speaking the one of most common kinds of visa that includes restrictions on working is visas for education (another common one is visas for temporary travel whether for business or pleasure, but while there may be more visas issued because people with these visas generally aren't staying, you are less likely to meet them or try to hire them), and it's common to travel for university-level education, more so for post-graduate education. So the largest population of foreigners which have restrictive visas is going to be post-graduates who are studying abroad. It's certainly the only situation where I have met someone who is legally in the country but I could not legally hire.
