In order to qualify for UI, the lower offer must generally be at least 20% below your current salary. However, before an offer can even be considered for purposes of UI eligibility, the offer must be "genuine." An oral offer with nothing more, provided by a person who may or may not have authority to hire, is not a genuine offer. So, if your employer is making you another offer, then tell them to put it writing, with a complete description of the job and benefits, or you will assume that the offer is simply an offer to negotiate.
Hope this helps.
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