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On the practical side, it seems pretty cut and dry. I should communicate with the person about performance problems (and expected changes) clearly and repeatedly. If things don't improve in a reasonable amount of time, having the person around isn't helping the business. Time to end it.
However, I feel like I would be devastated to lose a job in this way, so I feel sympathy. I know change is hard and takes time. I also know that letting someone go can affect morale on the team. Is it better to just pay the cost and keep the person around?
How do you decide when it's time to let someone go?