You have to ask yourself why you are being offered this?
Companies rarely do things without a reason that provides themselves with a benefit. Sometimes they are just nice, but if they just wanted to be nice they would say "we will not tell future employers that you were fired for poor performance". The offer they have made means that they want you to resign rather than be fired, and are prepared to offer you something you want in order to get it.
The usual reason companies offer like this is that they will owe you severance or other money if they fire you, and don't want to pay. That in turn means they can't prove to the satisfaction of their own lawyers that you really did perform poorly enough to deserve termination. (Your completing the PIP successfully would back up that idea.) Their lawyers are probably concerned that if they terminated you for performance you might make a successful legal claim.
An important question you should ask is
Will my termination be "for cause" or "not for cause"?
If you are terminated for cause then they do not have to pay you severance. But they do have to prove, if you dispute the termination in court, that they were justified in terminating you. If they terminate you without cause there is usually severance to pay. Also if they terminate you without cause then you can say that to a future employer, and they would understand that it means your previous employer couldn't find any legal reason to fire you.
Proving cause is hard, and many companies would rather pay the severance than try to prove it. Alternatively they want to persuade you to resign with inducements like this. If you resign then they don't have to pay you severance or prove your incompetence.
I hope it is obvious that if you resign you will not be entitled to unemployment benefits, which may be a big problem if you do not get a job for a long time. You also have no legal redress against the company.
Visiting a lawyer is probably a good idea, if only to get an idea of what you are actually entitled to if you are terminated or if you resign. Depending on how long you have been at the company tens of thousands of dollars may be at stake. If you have a contract read it carefully to find out what the company owes you for termination without cause. Have your lawyer read it too, if you visit one. Note that your contract overrides the "at will" nature of your employment.
As for what you should actually do, I would push back somewhat. Ask the question above. If they say they will fire you "without cause" then I would let them fire you. You will get unemployment benefits if you need them, and you can reasonably tell future employers that you did nothing substantially wrong to deserve being let go. (you won't be using this company as a reference.) You might gently suggest that you would consult a lawyer if you were fired "with cause".
If they threaten to fire you "with cause" then you can also negotiate the terms of your termination. You could agree terms of termination in which they still fire you (meaning you will get unemployment benefits) but you agree to severance that they are happy with, in return for them not saying you were fired for poor performance. The aim of your negotiations should be to be let go without cause (not resigned), with a promise of a reasonable reference, and with them paying you severance you both find acceptable (which may be zero). I went through this with a company (who were blatantly trying to get rid of me without any justification) and we agreed that they would give me one month's notice, without cause, and a month's pay after that. In fairness that was in Canada.
If you are in an "at will" state and you don't have a contract then much of this may not apply, but companies don't usually make offers like this unless they have a contract, explicit or implicit.