Usually people I had in my hearings would state their boss was verbally abusive. The persons in these types of cases had usually quit the job and had been found ineligible for benefits. First verbal abuse must be defined. Basically the only type the state recognizes is if you had been physically threatened. Simply being told you could be fired, or, you are not a good person etc does not count as verbal abuse. The definition can vary widely from person to person. Very rarely in these cases did the person work for a large company or corporation. For whatever reason it is much more likely to be from a small local business where the supervisor can get away with his or her actions with no repercussions. In that case, the person who believes they are abused has no one to report a complaint to and there is usually no human resources department.
If a person believes they are being abused in either situation they need to begin documenting everything. Also depending on your state laws, you may try secretly recording the person who is harassing you. I would advise you to research your state laws prior to recording someone so you are not violating the law yourself. Document all of your interactions with the person, what was said and when. Also, if you spoke to anyone else about the situation that should also be documented.
Rather than just quit without notice, or providing a resignation letter to the supervisor with no mention of why you are really quitting you could try the following. Present the supervisor with a letter of complaint and that if things do not improve in a certain amount of time that you would be quitting. This could cause one of a few things all of which should be beneficial to you. The person could become angry and fire you. Retaliation against you does not look good in an unemployment hearing. The situation could actually improve, this is probably the least likely to happen. Or, nothing changes, giving you good cause for quitting.