UI doesn't care if you're sick or if you had a death in the family. In most states, if you aren't available each and every day of the 7 days in a claim week, you are not "able and available" for that week, and you don't get a check for that week. So don't compound your problems by trying to explain that you got a full check because you called in sick and went to a funeral.

Also, why in the world did you take a 2-day a week job in NY? They have one of the worst partial benefit calculations in the country. They don't base it on earnings, but rather the number of days you work in a week. 1 day is a 25% reduction, 2 days is a 50% reduction, 3 days is a 75% reduction, 4 or more days and you get nothing. You can have a situation where a part-time job pulls you in for 10 minutes, you earn pennies, and then lose up to nearly $100 if you have a max benefit of $405/wk.

The lesson you really need to learn here is that part-time work and UI claims are generally headaches. A claimant can almost always refuse a part-time job because it is substantially less favorable than the prevailing conditions of work. However, after you accept it, the theory is that you know what you're getting yourself into so that acts as an acknowledgment that it is suitable employment for you, or you wouldn't have taken it.

While harassment and health and safety sound like good reasons to quit a job, the burden of proof is on you, and I suspect you'll have a tough time convincing anyone working in claims adjudication or a hearing officer that what you said was true without witness testimony, pictures, video, or recordings.

PandorasBox is right about the quitting a job in a short period of time if it's unsuitable, but I just wanted to say that I think that provision is rare. To date with her adding Michigan, these are the other states that I know of with that provision: ND, VA, WI, and MI