"By the sacred anointing of the sick and the prayer of the priests the whole church commends those who are ill to the suffering and glorified Lord, that He may raise them up and save them."
(Catechism of the Catholic Church 1499)
The request for a priest to administer the Anointing of the Sick should be made whenever a Catholic is seriously ill or in danger of death. The Sacrament should not be delayed until the final moment of someone's life.
The parish office should be alerted if a homebound parishioner would like a priest to visit them or for an Extraordinary Minister to bring them Holy Communion.