I have handled appeals of unemployment determinations and they sometimes do get overturned. If you have proper written verification that stress caused by your supervisor amounted to a "termination" in effect, it may be worth it to appeal.
Mark L. Rosenberg is an attorney admitted to practice in the State of Maryland and the District of Columbia only. This answer is meant to be for educational purposes and no attorney/client relationship is intended or created by this answer. You should consult an attorney in your jurisdiction for information on your case or claim.