What about? I would pray for his/her conversion to the One, True Faith before his/her expiration. That's the Catholic "thing" to do.
Yes; there are a number of Catholic things to do. There are the Seven Penitential Psalms. There is the Rosary. There are short aspirations: "Trust the Lord: He is trustworthy. Trust Him with all your heart." There are prescribed prayers for the dying, in fact, commending the soul to Divine Mercy.
All this is done in the realization that the man (it's always been a man) may not be conscious of what you're saying: his cognitive powers are usually much impaired. That's why touch (holding his hand, for instance) is so important.
And sometimes I sing.
Jesus, my Lord, my God, my All,
How can I love Thee as I ought?