The liability of an employer prescribed by this chapter is exclusive and in the place of any other liability to such employee, personal representative, surviving spouse, parent, any child, dependent, next of kin, or other person entitled to recover damages on account of such injury or death. If an employer other than the state or any municipal subdivision thereof fails to insure or self-insure liability for compensation to injured employees and their dependents, an injured employee, or legal representatives or, if death results from the injury, any dependent may elect to claim compensation under this chapter or to maintain an action in the courts for damages on account of such injury or death. In such action it is not necessary to plead or prove freedom from contributory negligence. The defendant may not plead as a defense that the injury was caused by the negligence of a fellow servant, that the employee assumed the risk of employment, or that the injury was due to the contributory negligence of the employee, unless it appears that such negligence was willful on the part of the employee. The burden of proof to establish such willful negligence is upon the defendant. For the purposes of this chapter the state and each municipal subdivision thereof is treated as a self-insurer when not carrying insurance at the time of the injury or death of an employee.