When the amount of co-payment made in relation to the payment of benefits for medical treatment or the amount calculated by deducting, from the amount of expenses incurred in medical treatment (excluding dietary treatment and living support), an amount equivalent to the amount paid as medical expenses combined with treatment outside insurance coverage, medical expenses, medical expenses for home-nursing, dependent's medical expenses, dependent's medical expenses for home-nursing, or special medical expenses (in the following Article referred to as the "amount of co-payment pertaining to specially-insured day laborer") pertaining to a specially-insured day laborer is extremely large, high-cost medical expenses are paid to the specially-insured day laborer who received benefits for that medical treatment, or the payment of the medical expenses combined with treatment outside insurance coverage, medical expenses, medical expenses for home-nursing expenses, dependent's medical expenses, or dependent's medical expenses for home-nursing, or special medical expenses.