Most of the time, when your employer truly thinks that about you, they'll work on your improvement informally. I don't like saying this, but I think most people's best interests are served by the assumption that a PIP signals their employer's transition from "working to retain them" to "working to manage them out of the company".
In the places I've used PIP's we used them mainly on staff we hoped to get to a level where we could promote them. We didn't waste time on proper PIP's for people we wanted to manage out - for those people HR simply mandated no raises ever. They'd leave or gradually get cheap enough for what they delivered to be worth having around.
EDIT: It's worth noting that in these cases the staff in question also had clear evidence in the form of signed reviews rating them that they were performing well. E.g. the guy I spent most time on a performance improvement plan for was ranked "exceeds expectations" in every criteria three years in a row while I was there, and was given 15%+ raises each of those years. This was in Europe, but for a US company.
On the off-chance they're doing that because your performance is abysmal and you haven't improved enough from their informal intervention, if in PIP you managed to finally recover your performance, maybe they will let you stay a bit longer.
I was the recipient of a PIP at my last job, went through the improvement process, and at the end of it, my manager signed off that my performance had returned to acceptable levels. I left about a month later.
So why am I not still there? Well, in the process of going through the PIP and asking myself how I let things get to that point, I realized that I was quite capable of excelling at everything I was supposed to be doing, but I just didn't give a shit anymore. My subconscious had already checked out of that job and was telling me it was time to move on.
When I realized that, my reaction was to start looking for another job while bringing my performance back to a good level. We quit on good terms: they "hired" me back to consult on some problems that came up after I left; I helped someone transition into my old position and I have a job better suited to my personality.
By the way, you don't have to sign the PIP. In fact, you shouldn't, because if you do, you're basically admitting that, yes, your performance is indeed low and needs improvement. And that goes in your employee file.
The right thing to do is to take the paperwork and say, "thanks, can you give me a few days to review this?" and stall as much as possible while looking for another job.
If you're feeling especially ballsy (and very confident in your ability to find another job quickly) you can say, "I'm not familiar with these at all, and my grandpa (R.I.P) always told me to get everything reviewed by an attorney before signing it, so that's what want to do. Is that OK?"
