I wasn't talking about reapplying though. You have no obligation to apply. Former employers, family and friends that "refer" you to work don't count. However, a potential employer does have the right to make you an offer regardless that you didn't apply.
I was faced with a buyout situation. I was praying the buyer would ask us to apply because I wasn't going to. Unfortunately, the buyer gave me a letter offering me my exact same job and that nothing would change. I couldn't refuse it and expect to get UI based on the "refusal of work" issue that was sure to follow. However, if things were just slightly less favorable to me, I'd have taken the chance and refused. In the early days of a UI claim, the job better be very close to what you just lost. One of the goals of the UI system is "not to depress wages." If it were any other way, employers could entice employees with slighty higher salaries, and once they had you, they could lower your pay to less than market rate, and while legal, it's not a reason to be denied UI when you refuse.