Thank you for your reply. It would seem then that you have two questions--first, whether the severance agreement is enforceable, and second whether you can collect unemployment if you refuse to move out of state.
With regard to your first question, verbal employment contracts
--including severance agreements--are generally enforceable, and so if your employer promised you a severance payment in exchange for continuing to work additional time, and you relied on that agreement by agreement to work additional time, your employer would be legally obligated to pay your severance.
From a practical standpoint, however, you may have a problem with proof. If you had any sort of email or text message corroborating the agreement, that would be helpful. If co-workers will testify that the agreement was made, that would also be helpful. If all you have is your personal testimony, you can still certainly bring the claim, but it will be " word against word," and so success of the claim will not be guaranteed.
With regard to unemployment benefits
, the good news there is that an employee who refuses a relocation out of state will almost certainly still retain his or her eligibility for unemployment, even if the employer wants to characterize the refusal as a "resignation." While individuals who resign are normally disqualified from benefits on the ground that they became unemployed through fault of their own, an employee who refuses out of state work typically does so with "good cause," since employees can't simply be expected to uproot their entire lives to follow their jobs, and a resignation in such circumstance is thus with "good cause."
I'd just want to make sure it's very well documented that your employer is insisting you move out of state and that this is the basis for your quitting.
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