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It depends on the nature of the severance.
For instance, if you gave notice and the employer stated that they wanted you to leave but that they would pay you through the notice period, that is not severance. It's pay in lieu of notice
and you wouldn't be entitled to unemployment during that time.
Additionally, continuation pay at the end of employment, with full benefits, that was part of a guaranteed plan (usually seen in collective bargaining agreements, where certain classes of employees would be guaranteed continuation pay that the end of their employment) would disqualify someone from unemployment.
However, individually negotiated severance does not disqualify one for unemployment benefits
. It should be reported at first, with unemployment, when filing and once it is determined that it is regular severance, there would not need to be further reporting of the income from the severance.