The Sacred Heart devotion is a beautiful one, and a great reminder of God's love and mercy towards sinners.
St. John Paul II mentioned this aspect of the Sacred Heart devotion in a letter on the 100th Anniversary of the Consecration of the World to the Sacred Heart:
The Savior's Heart invites us to return to the Father's love, which is the source of every authentic love: "In this is love, not that we loved God but that he loved us and sent his Son to be the expiation for our sins" (1 Jn 4:10). Jesus ceaselessly receives from the Father, rich in mercy and compassion, the love which he lavishes upon human beings (cf. Eph 2:4; Jas 5:11). His Heart particularly reveals the generosity of God towards sinners. God's reaction to sin is not to lessen his love, but to expand it into a flow of mercy which becomes the initiative of the Redemption.
This is good news especially for us, as we need to remember that we are always included in the list of "wandering sheep." We may try to stay faithful to Jesus Christ, but every time we sin, we walk away from God in some way.
Here is prayer from the Raccolta, a collection that dates to the early 20th century, asking Jesus to bring together all "wandering sheep."
O Lord Jesus, most merciful Savior of the world, we beg and beseech Thee, through thy most Sacred Heart, that all wandering sheep may now return to Thee, the Shepherd and Bishop of their souls. Who lives and reigns with God the Father and the Holy Spirit, God for ever and ever. Amen.
