In each of the ‘last rites’ I have used the wonderful centuries old ‘sending on’ prayer the Proficiscere (here in a shortened version) - Go forth from this world, O Christian soul: in the love of God the Father who created you, in the mercy of Jesus Christ who redeemed you, in the power of the Holy Spirit who strengthens you. May the heavenly host sustain you and the company of heaven enfold you. In communion with all the faithful, may you dwell this day in peace. Amen.
Like all the sacraments, holy anointing was instituted by Jesus Christ during his earthly ministry. The Catechism explains, "This sacred anointing of the sick was instituted by Christ our Lord as a true and proper sacrament of the New Testament. It is alluded to indeed by Mark, but is recommended to the faithful and promulgated by James the apostle and brother of the Lord" (CCC 1511; Mark 6:13; Jas. 5:14-15).
[Catholic Teaching] The Sacrament of Anointing of the Sick is meant for anyone who feel ill to the point of fearing death, and if indeed they do die, the Sacrament is a blessing from the whole Church that God will lift them up and save them in the Kingdom of Heaven.