Christ was offered once to exhaust the sins of many; the second time He shall appear without sin to them that expect Him, unto salvation.
Verse 28. To exhaust the sins of many. That is, of all, according to the style of the Scriptures. When he came first, he took upon him the load of our sins; but at his second coming, at the end of the world, he will come in a quite different manner, not as laden with our sins, not after the similitude of a sinful man, not to redeem us, but with great power and majesty to judge all men. Wi. — To exhaust. That is, to empty or draw out to the very bottom, by a plentiful and perfect redemption. Ch.
COUNCIL OF VALENCE III 855 (Against John Scotus)
Can. 4. Likewise concerning the redemption of the blood of Christ, because of the great error which has arisen from this cause, so that some, as their writings indicate, declare that it has been shed even for those impious ones who from the beginning of the world even up to the passion of our Lord, have died in their wickedness and have been punished by eternal damnation, contrary to that prophet: “O death, I will be Thy death, O hell, I will be thy bite” [Hosea 13:14]; it seems right that we should simply and faithfully hold and teach according to the evangelical and apostolic truth, because we hold this price to have been paid for those concerning whom our Lord Himself says: “As Moses lifted up the serpent in the desert, so it is necessary that the Son of man be lifted up, that all, who believe in Him, may not perish, but may have eternal life. For God so loved the world that He gave His only begotten Son: that all, who believe in Him, may not perish but may have eternal life” [John 3:14 ff.], and the Apostle: “Christ,” he said, “once has been offered to exhaust the sins of many” [Heb. 9:28]. Furthermore, although they are becoming widely spread, we completely remove from the pious hearing of the faithful the chapters (four, which by the council of our brothers have been unwisely accepted, because of the uselessness or even the harmfulness, and the error contrary to truth, and other reasons) absurdly concluded with nineteen syllogisms, and not outstanding in learning, in which the machination of the devil rather than any tenet of faith is found, and that such and similar things may be avoided through all (chapters), we by the authority of the Holy Spirit forbid (them); we believe also that those who introduce these novel doctrines must be punished lest they become too harmful.
940: The Sacrifice is a Visible Propitiation for the Living and the Dead
SESSION XXII (Sept. 17, 1562) The Doctrine on the Most Holy Sacrifice of the Mass
And since in this divine sacrifice, which is celebrated in the Mass, that same Christ is contained and immolated in an unbloody manner, who on the altar of the Cross “once offered Himself” in a bloody manner [Heb. 9:27], the holy Synod teaches that this is truly propitiatory [can. 3], and has this effect, that if contrite and penitent we approach God with a sincere heart and right faith, with fear and reverence, “we obtain mercy and find grace in seasonable aid” [Heb. 4:16]. For, appeased by this oblation, the Lord, granting the grace and gift of penitence, pardons crimes and even great sins. For, it is one and the same Victim, the same one now offering by the ministry of the priests as He who then offered Himself on the Cross, the manner of offering alone being different. The fruits of that oblation (bloody, that is) are received most abundantly through this unbloody one; so far is the latter from being derogatory in any way to Him [can. 4]. Therefore, it is offered rightly according to the tradition of the apostles [can. 3], not only for the sins of the faithful living, for their punishments and other necessities, but also for the dead in Christ not yet fully purged.