A firefighter shall remain eligible for benefits pursuant to subsections (1) and (2) of section 35-1005 for thirty-six months after the formal cessation of the firefighter's status as a firefighter. If a firefighter has a physical examination during the thirty-six months of eligibility that reveals evidence of cancer, the firefighter shall be eligible for benefits under subsections (1) and (2) of section 35-1005 even if such benefits are paid after the thirty-six-month eligibility period ends. The rural or suburban fire protection district, airport authority, city, village, or nonprofit corporation for which such firefighter served shall be responsible for payment of all premiums or other costs associated with benefits that may be provided under subsections (1) and (2) of section 35-1005 throughout the duration of the firefighter's coverage.