Once the PIP starts, start asking coworkers you trust if they'll provide a reference and looking for a new gig. Your chances of coming back from a PIP are non-zero, but at the same time exceedingly low. You'll expend less effort moving to another gig with a chance you'll land with a better skilled manager (assuming your manager is the problem, and not you). You might even get a salary/comp bump out of the move.

This advice is more valid in our current, exceedingly tight, labor market and less so when unemployment goes up again (be prepared for a longer search, network more aggressively, and have a longer emergency fund runway).

I wouldn't b surprised if lots of people comes back from a PIP. But I would be surprised if my co-workers were bragging about that time they survived a PIP.

ie. it's likely we believe the odds to be low, because it's not something people talk about.