At most public universities, the tenure track faculty, staff, and admin are primarily jobs negotiated through the public union. They are paid for by tuition revenue and state funding. They cannot legally be cut, and almost always are directly related to the teaching aspect of a university.
However, universities do research, and need research infrastructure. This includes administrators, safety people, compliance people, core research facilities, etc. Those are usually on what is called "soft money" - funds from IDCs. Those folks can be eliminated, of course, but there are typically very few of them and they are serving the most essential roles. If you eliminate them, you may need to eliminate your research program altogether. The NIH requires you to meet safety standards, the EPA requires specific waste disposal, etc. The folks that ensure that compliance generally are paid for by IDC funding.
