When are the "Last Rites" given?

The term “Last Rites” refers to the last rituals of the Church. If a Catholic person is alive and near death they should receive the Anointing of the Sick and the Final Blessing, if possible. But many people have already been anointed. The “Last Rites” are celebrated at the Funeral, or Mass of Christian Burial.

What happens if a person does not have a blessing of a Priest at their death?

This is a worry for some people. However, one who is living the Christian life, receiving God's Grace in His Word, Sacraments and in other ways is not "in trouble" with God if there is not a Priest present at death. The Lord is present in the life of the person. Any person who is beloved of God and who truly wishes to love God is welcomed into His Kingdom.