In addition to any other payments authorized to be made from the fund established under § 28-37-1, payments from the fund shall be made for the continuance of compensation and medical expenses at his or her prevailing rate to any employee who subsequent to January 1, 1940, has suffered an injury resulting in his or her receiving compensation payments for total incapacity and that incapacity has continued or will continue beyond the maximum period of payment for total incapacity provided under chapters 29 — 38 of this title. The payments for continuing total incapacity shall be made from the fund until the employee’s total incapacity has ended or the employee’s claim has been settled pursuant to § 28-35-20 or until his or her death. No payment shall be made under this section to an employee whose future payments of compensation have been commuted to a lump sum. The death of the employee from any cause terminates the right to any further compensation under this section.