Is an employer required to pay severance?

No.  An employer has no legal obligation to pay an employee severance, unless there is a contract, severance policy, or severance plan that creates a contractual entitlement to severance pay.  Some severance plans provide that severance is within the sole discretion of the employer to pay or not pay.  Severance plans may also disqualify an employee from any entitlement to severance for various reasons, most commonly termination for cause or voluntary resignation.