The real purpose of the PIP process is to grind people down so they make mistakes, costing them what could otherwise be beautiful lawsuits [1], or just stop showing up (which I guess would fall under quitting, since they end up firing themselves, at least bureaucratically speaking).
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[1] This is surprisingly easy to do in the US. If you post about your termination on social media, this can be construed as "cause after the fact" and make a termination that was in fact unjust or unlawful now legal. The employer's argument becomes that they knew you held malice toward the company ("cause") but couldn't prove it--the social media activity becomes said "proof".