Any employer subject to this chapter who procures and continuously maintains workers’ compensation insurance as required by this chapter or who elects to make direct payments of compensation as provided in this section is not liable to respond in damages at common law or by statute for the injury or death of any employee, however occurring, after so subscribing or electing, and during any period in which the employer is not in default and has complied fully with all other provisions of this chapter. Continuation in the service of the employer shall be considered a waiver by the employee and by the parents of any minor employee of the right of action as aforesaid, which the employee or his or her parents would otherwise have: Provided, That in case of employers not required by this chapter to procure and maintain workers’ compensation insurance, the injured employee has remained in the employer’s service with notice that his or her employer has elected to procure and maintain workers’ compensation insurance, or has elected to make direct payments as aforesaid.