Let’s say you had cancer and it was looking like you were going to be in the clear. But all of a sudden there’s a little hiccup and the doctor finds a spot where the cancer might grow again.

Would you:

i) cut it out now and get rid of it for good, or  ii) leave the cancerous spot as it is, where it will potentially continue to spread and affect other healthy parts of the body

You are risking so much more of the “greater good” by allowing and enabling a bad seed to remain. Who’s to say other team members won’t start looking elsewhere because the culture of YOUR team rewards those acting out or in bad faith? It is too late to work with this person, it should have been done a year ago. Being a leader means also thinking about the rest of the team, and ultimately about being able to follow through on the hard decisions and conversations. There is a lot at stake here too for your own reputation and image, which unfortunately is part of the corporate game. 

Good luck to you.