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Unemployment benefits are reserved for individuals unemployed "through no fault of their own." When an employee voluntarily ends their employment, they will be deemed unemployed "through fault," and denied benefits on that basis.
What is problematic about the language of the separation agreement you are quoting is that it indicates that you are "agreeing" to end the employment. That, in isolation, would support the denial of benefits because if you are "agreeing" to end the employment you are unemployed "through fault."
The good news is that the unemployment office will not view something like this in isolation. They base eligibility on whether you are ACTUALLY unemployed through no fault of your own, not what your separation agreement may or may not say about it. So, if you can prove through other means that this was actually an involuntary separation, then you can still be approved for benefits.
Therefore, the best course of action would typically be to create documentation to support that your separation is not voluntary. This can be as simple as an email to your employer reiterating that you would like to remain employed but since there is no work for you that you are willing to sign the severance agreement and move on. In short, if you have some way of proving that this is an involuntary separation, signing a severance agreement with the language you describe would not typically result in disqualification from benefits.
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