Soft money supported versions are fairly common - mine's got a substantial hard money component, which is what makes it rare and honestly a little bit wonderful.
Soft Money: A position where a substantial portion (usually 50%+) of one's salary is expected to be brought in by grants. Failing to do so is, at best, going to impact your salary, and at worst, is a good way to no longer have a job.
Hard Money: University-level funds (from the university, the state if a state school, etc.) provide a portion of your salary that doesn't have to be tied to a grant. This often comes with other obligations (i.e. teaching).
Most positions are a mix of the two in some form. Purely soft money positions, or >50% soft money positions, are common at some research institutes, medical schools, etc. Hard money positions that don't come with substantial non-research obligations are very rare.
