Defense usually wins if they have good documentation of putting employees on a PIP, even if the reason is obviously dubious*.
Maybe I'm cynical because I've only seen it in a lawsuit context, but if you're put on a PIP, start applying. There's no out.
* like, discrimination, company wants to fire long-term employee because of an injury, company wants to fire an employee for union organizing, etc.
I'm a manager at Google and have therefore been privy to a bunch of PIPs. I know a bunch of people who have survived them and many of them have later gone on and had successful promos. I've seen exactly one case where everybody involved was resigned to the fact that the PIP would almost certainly fail and that is because the person being fired was a raging asshole. A manager who wrote a PIP designed to be impossible would themselves be given shit performance reviews.
A PIP isn't just a closed two-way conversation between a report and a manager. In every case I've seen there are multiple eyes on a PIP and revisions to them.