It appears that things are irreparable. Don't resign, ask them to give in writing reason for PIP. Counter on that email also mention in that response that you were asked to resign in lieu of PIP. Also mention that you will explore legal options due to unlawful termination. Get a Psychiatric evaluation stating you have developed depression due to turmoil in professional life. Send that certificate to HR and Legal top brass. Again mention you will seek legal remedies. Keep copies of all correspondence. Starting now, also search for a job.