It depends on how much lower, especially how much lower the pay is. As a rough rule of thumb (every case is judged on its own facts and circumstances, so we can't articulate some "bright line" rule), if your pay is being cut by 1/3 or more, it is likely that you could quit and get unemployment on the grounds that you were "constructively"--or effectively--terminated by the job being changed in a way no reasonable person would accept. Less of a decrease than that, however, and if you quit or resigned, it would most likely be considered a voluntary separation from employment and you would not be eligible for UI.If you refuse the demotion but not quit and then are fired, you would be eligible for UI; being fired because you will not accept a demotion is not a "for cause" (for doing something demonstrably wrongful, like violating company policy, open insubordination, absenteeism, false time sheets, etc.) firing, and when you are terminated not for cause, you can get UI. So you can refuse and take the chance of being fired, if you are willing to lose your job and be on UI instead of taking the demotion.