If the person in a nursing home is chronically ill or aware that the stay will be permanent, the Icelandic Health will pay 100% , otherwise the patient will pay his/her share in accordance with rules on pensioners. See here.

Chronically ill: A recipient of an old-age or disability pension who spends more than one consecutive month in a hospital that is on a fixed budget and whose stay has lasted longer than six months during the previous twelve months. The same applies if it is clear from outset that the nursing home or nursing home in an aged care institution is permanent compare 4 of Article 48 of the Social Security Act no. 100/2007.