Jesus came to heal the whole person, body and soul.
In the Church's Sacrament of Anointing of the Sick, through the ministry of the priest, it is Jesus who touches the sick to heal them from sin – and sometimes even from physical ailment. His cures were signs of the arrival of the Kingdom of God. The core message of his healing tells us of his plan to conquer sin and death by his dying and rising.
The Rite of Anointing tells us there is no need to wait until a person is at the point of death to receive the Sacrament. A careful judgment about the serious nature of the illness is sufficient.
When the Sacrament of Anointing of the Sick is given, the hoped-for effect is that, if it be God's will, the person be physically healed of illness. But even if there is no physical healing, the primary effect of the Sacrament is a spiritual healing by which the sick person receives the Holy Spirit's gift of peace and courage to deal with the difficulties that accompany serious illness or the frailty of old age. Catechism of the Catholic Church - usccb
376 The blessing of the sick by the ministers of the Church is a very ancient custom, having its origins in the practice of Christ himself and his apostles. When ministers visit those who are sick, they are to respect the provisions of Pastoral Care of the Sick: Rites of Anointing and Viaticum, nos. 42-56, but the primary concern of every minister should be to show the sick how much Christ and his Church are concerned for them. 377 The text of Pastoral Care of the Sick indicates many occasions for blessing the sick and provides the blessing formularies. 378 The present order may be used by a priest or deacon. It may also be used by a layperson, who follows the rites and prayers designated for a lay minister. While maintaining the structure and chief elements of the rite, the minister should adapt the celebration to the circumstances of the place and the people involved. 379 When just one sick person is to be blessed, a priest or a deacon may use the short formulary given in no. 406 Order for the Blessing of the Sick | USCCB