Employee you can't fire?
and they know it?
Don't get all tooboring on me, this is the real world ..
In business, I can think of a few things, but not many, that are as bad.
I have endured bad employees who thought they were irreplaceable, and they cost me both financially and mostly personally because of the stress and management challenges that they presented.
I won't give you the glib business coach answers, just the battle scarred veteran advice:
There isn't anyone you can't fire. There are just people that will make it emotionally difficult, or from a business perspective, management challenging, to replace.
When you are sick and tired of being sick and tired of them, you will do it.
You just have to be ready to endure the temporary (and it is temporary) pain to get through it.