How do you know when terminating an employee is the right decision?

Usually you start the PIP because you really want the person to leave.

Interesting approach. I think in most cases PIP is really a euphemism for the last official warning (something that HR might need to do to comply with policy and to manage risk). If it has come to that point it means that initial attempts at coaching/mentoring failed. If an employee is surprised we have a failure of management.

I agree with you, you're not doing them any favors by keeping them around. I've also run into this scenario a few times where somebody is unable to accept the positive aspects of change. At a former company that had just gone through a dark era, the senior leadership were setting things right and things were going much better. It had been better for over a year, but this person was still being negative. Finally we just said, "Today's your last day." They were dragging everybody else down and they were not being successful themselves.

It's not fun to terminate someone but it's more painful to keep them on board, especially when people have to work harder around that person. That's another termination scenario I’ve been through: everybody else had to work harder to keep this person on staff because they were just dropping the ball. Other team members ended up spending more time cleaning up after this individual than they did doing anything else, so it created negative output.