Outside of someone protected by a labor union, I’ve very rarely seen anyone recover from a PIP and not be eventually let go. Most commonly employees see them as a 30 or 60 day window to proactively find a new job before they’re terminated.
For example, a friend I have that recently left Facebook knew for a good 6 months he needed to shape up. But they hadn't put him on a PIP in that time. They eventually offered him a decent severance to quit, and he took that rather than continuing to try. If he stayed, he probably would have been put on a PIP fairly shortly. It was the best thing for everyone. He wasn't all that happy there anyways.
Lots of people bad at their jobs blame the PIP system for their failure at Amazon.