Common reasons why people who should have been fired a long time ago aren't:
Internal politics - can be interdepartmental scuffles, friendships with people in high places (or blood or marital relations), a manager who protects them from consequences, or any number of other factors.
External politics - they may be related to a donor or some other benefactor, have a public-facing role with a lot of community ties, possess a great deal of prestige in their field (particularly in academia), or otherwise have the potential to trigger a major backlash of some sort.
Business needs - they may simply be too good at their jobs to fire, or have too many established relationships with clients, vendors, and/or donors that the company doesn't want to hurt.
Gun-shy HR - they may be hamstrung by burdensome company policy or employment law and know that they will not be able to fire someone for anything that isn't truly egregious, the person might belong to a protected class, have a proven history of litigiousness, or already be in a dispute with the company where a termination would look extremely suspicious, or the company may have just lost big on a wrongful termination claim and is being overly cautious for liability purposes.
Union issues - the union may have a historically poor relationship with management and is loath to side with them, they aggressively fight any sort of disciplinary action, the person knows how to game the disciplinary process, or the person is a high-ranking official.
The need to buy silence - the person knows about something illegal or immoral (or, barring that, extremely unflattering and likely to cause a PR fiasco) that is going on, or was an active part of it, and it's crucial to keep them happy so that they don't start talking.
Tenure, though this is not an absolute shield - egregious misconduct is a common reason, and downsizing or elimination of a program is a perfectly legitimate and protected reason to let go of tenured faculty, provided that it is not a ruse to get rid of tenured faculty without due process.
