By “work” do you mean doing something during the day that gets you paid. In the United States, or in the Israeli universities, once you receive money in excess of tuition or waived room and board fees, you are considered an employee. In Israel, if such persons are employed by the teachers, they are not considered employed. While in English there is a clear distinction between student and teacher, in traditional Hebrew, a “Ben Yeshiva” could mean either. Bnei Yeshiva who receive enough money to support a family are employed, even if the green eyeshade guys don’t count them. In addition a great many yeshiva “students” have jobs off the books since if they worked on the books, they would be drafted into an army that is incredibly hostile to bnei Torah.
If the government wanted most of the bnei yeshiva to be part of the economy, they could exempt them from the army (perhaps tied to being fathers, a grounds for exemption in many countries with conscription).