Besides all the reasons here why the system is broken, academia is also frequently a source of free/cheap labor from students trying to publish something or just get some experience.
So, at least where I came from, in the constant presence of fund cuts, the PI just replaces whoever lost their grant with a volunteer student, or perhaps keeps that person working for free with the perspective of finish and publishing the work or with the vain hope that he/she'll get paid when the next round of funding comes.
No matter what, the PI gets his name on every paper and also his salary (in most cases, that is).
Seems not surprising that people start leaving this "profzi" scheme (http://www.phdcomics.com/comics/archive.php?comicid=1144).