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The general rule is that employment in the state of NJ is "at will" absent an express agreement to the contrary. At will employment can be terminated or modified for any reason not amounting to discrimination on the basis of a legally protected trait (race, religion, gender, etc.) or retaliation for engaging in certain forms of legally protected conduct (filing a wage claim, taking FMLA leave, etc.). It doesn't matter whether the basis for termination is fair, reasonable or even true. It also doesn't matter whether the employee had a specific job description--job descriptions have no legal force or effect unless that specific job is guaranteed for a set period of time.
Now, as for whether the employee would be eligible for UI benefits if they quit due to a change in their job, the answer is "maybe." It depends on whether the State finds that the change in job duties was so significant that no reasonable person genuinely desirous of remaining employed woulf have done so. For example, if someone was hired as a manager and then gets demoted to janitor, they would likely be eligible for unemployment benefits because no reasonable person would accept that change. The example you give is a little less clear, and ultimately it's impossible to predict what will happen since these things are judged on a case by case basis.
Generally, it's best to accept the change in duties and quit only once you've secured alternative employment. That way you don't have to take the risk that you will be denied benefits and have no way to support yourself. Also, it is generally easier to find a job when you are already employed. It has something to do with employers wanting to hire those whom they perceive to be "in demand." Still, the choice would be yours to make if you feel you can argue that no reasonable person would accept this change in job duties.
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