How to get rid of a problematic employee?

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I was discussing with a few of my senior managers the other day in regards to someone who used to work for our company. This someone was a very problematic person and plainly a weirdo. He used to stand behind a female colleague for 30 minutes without saying anything and without moving at all. My female colleague nearly fainted when she turned around to see this guy standing behind her. The guy also cannot look straight to anyone during conversation and he even harassed some people. But this is an extreme case. There are also incidents where an employee just do not perform at all even though you give the person a lot of warning letters. Terminating the person is the last resort which you will use, but avoid using it. So how do you think you can get rid of a problematic employee without terminating the person? It's not cheap to terminate someone.