depends on the state in the US. And let's say the HR dept has performance issues. How do you fire someone in HR? They're the ones that know all the rules and all the laws that could get you in trouble. Where I work slid by, managed to can the HR head, but they were only able to do it because 1) she was super-overpaid and there was a budget crunch - which can be a legal problem for nonprofits (overhead) 2) there was a pretty serious SNAFU involving federal funds that happened under her watch, so she could have been in legal trouble herself.
Also, gross incompetence is not necessarily the problem... Death by a thousand cuts.
Also, gross incompetence is not necessarily the problem... Death by a thousand cuts.