Can I get legal help if I haven't been fired yet? I have some evidence that may come in handy for a legal case.
Absolutely. There are lawyers who specialize in this sort of thing, and they can give you a good perspective on how the laws work where you live. An hour-long consult would be an excellent investment.
Quietly collect and preserve whatever evidence is available: copies of your recent performance review, any documents related to the PIP, emails voice mails, whatever. This may be considered removal of company records, but they're going to fire you anyway. (If you retain counsel, ask how this should be handled. I'm not a lawyer and don't play one on the Internet. My advice is worth exactly what you paid me for it.) If you find yourself going after the company for wrongful termination, its existence will help in building your case.
To address a comment you made about another answer that I think needs to be part of the question:
If I quit I probably can't collect unemployment. If I'm fired without making an effort to comply with the PIP, again I probably can't get unemployment. ... I feel like they are just trying to make it impossible for me to collect unemployment or negotiate a severance package.
Severance packages are for employees not terminated for cause. Unless your company has a contractual obligation to provide one in this situation, you won't be getting one.
Being fired for cause doesn't automatically bar you from collecting unemployment benefits, and you should definitely apply. Give the unemployment commission as detailed a description of your termination as you can with, if your lawyer thinks it won't land you in hot water, as much evidence as possible. The process in most states is that your claim is initially considered valid and your company will have to contest it. Contesting a claim will cost them time and money. If your story is truly as described, they may think twice about committing perjury and decide against it just to get you out of their hair.
Your success in applying for benefits may be a good litmus test for how well a wrongful termination suit will go. As always, consult counsel.
But I can't comply without signing and admitting to wrong doing.
You're being forced into a catch 22. There is, as others have pointed out, no way to resolve this situation in a way where you remain employed.
I can't stress this enough: do not ever sign your name to a statement which isn't true, even if it means the loss of your job. If they fire you and you have to discuss it with someone later, you will be able to say "I was asked to sign a false statement and refused to do so." You want to come out of this as squeaky-clean as you can; this is an opportunity to force the company into being the party doing all of the wrong things.
If you're going to provide them with a statement, write one that fully describes the situation and indicates that you refuse to sign anything to the contrary. Send it to the company via certified mail so there's a record that you sent it and that the company received it.