To answer your question (sort of): in my state it is not possible. It is state by state; my state is "at will" employment. This means, in my state, you can be fired just because. Employers in my state can't violate federal law of course -- they can't discriminate etc -- but they can fire you because "you're just not good enough" with no details or documentation.

That said, it is likely CA has it's own set of protections that make it harder to do.

Usually, it's the company's internal policies that require a PIP and all the documentation even in an "at will" state. This is to maintain the appearance of fairness and to avoid the possibility of employment litigation (companies of course often operate in many states and federal law is always a concern). If you document, you avoid all this. The firing though is usually a _fait accompli_; the PIP is CYA.