Fiduciary liability insurance protects companies when there has been a breach of fiduciary duty. A breach of fiduciary duty is a serious infraction that can result in a lawsuit against a company and any individual with fiduciary responsibilities.nA fiduciary liability insurance policy covers a wide range of errors considered a breach of duty, including improper advice, wrongful denial of benefits, improper change of benefits, poor choosing or overseeing of the plan’s service provider, errors in administering the plan, and the mismanagement of the plan’s assets.