[Jtsummers]

I was that guy once, caused (in my case) by handling severe anxiety poorly. I recognized it and went to my boss, then therapy, and got better (both at work and personally). But if they're not recognizing or acknowledging their performance problems, you need to intervene. Ask them what's actually going on. Document responses and issues. Offer to lighten their load while they deal with whatever it is. Give them a reasonable amount of time to get back to work.

But make it clear that they're on a performance improvement plan, and if they don't meet the expectations after giving them some time, then they will be removed from their position or let go. It's not fair to the rest of the team to answer to someone who isn't behaving properly and it will hurt their morale and performance after a while.