I came across this the other day when reading St. Thomas’ Commentary on Hebrews – the flesh of the high priests’s sacrifice on the Day of Atonement remaining uneaten signified that the saved do not partake of the Old Law. Fascinating!

“743. – Then when he says, We have an altar, from which they have no power to eat who serve the tabernacle, he gives the reason, and it is quite subtle. For, as it is stated in Leviticus (chap. 16), on the tenth day of the seventh month the high priest entered with the blood of a heifer and a goat into the holies because of his own ignorance, and burned their bodies outside the camp. And because it was the priest’s offering, the flesh was not eaten. For whatever they offered for the sin of the priests they did not eat, but burned outside the camp. From that figure the Apostle draws a mystery. For the blood of Christ was prefigured by the blood, as was explained in chapter 9. The heifer and the goat prefigured Christ, because the heifer was the priest’s offering and the goat was immolated for sin. This prefigured that Christ would be immolated for sin: not for His own but for the people’s. Therefore, the immolated heifer and goat is Christ, the Priest, offering Himself for our sins. Therefore, the blood of Christ was brought into the holies and the flesh burned outside the camp. Two things were thereby signified: one, that Christ was immolated in the city by the tongues of the Jews; hence Mark says that He was crucified at the third hour, although He was raised on the Cross at the sixth hour. The other is that by virtue of His Passion Christ brings us within the heavenly holies to the Father. But the fact that the bodies were burned outside the camp, as to our Head, signifies that Christ would suffer outside the gate; but as to us, who are the members, it signifies that Christ is immolated for those who are outside the camp of ceremonies of the Law and of the external senses. For those within the camp did not partake of that flesh. This, therefore, is the figure which the Apostle proposes: first, therefore, he shows what is signified; secondly, he presents the figure (v. 11); thirdly, he draws the conclusion (v. 13).

744. – He says, therefore: Let us strengthen our hearts not with food, but with grace; for we cannot do otherwise, because we have an altar, from which those who serve the tabernacle have no right to eat. That altar is the Cross of Christ, on which He was immolated; or Christ Himself in Whom and by Whom we offer our prayers. This is the golden altar spoken of in Rev (chap. 8). Of that altar, therefore, they have no right to eat, i.e., to receive the fruit of Christ’s passion and to be incorporated into Him as head, who serve the tabernacle of the ceremonies of the Law: ‘If you be circumcised, Christ shall profit you nothing’ (Gal. 5:2). Or they serve the tabernacle of the body, who pursue carnal pleasures: ‘Make not provision for the flesh in its concupiscences’ (Rom. 13:14). For such persons received no profit: ‘He that eats and drinks unworthily, eats and drinks judgement to himself’ (1 Cor. 11:29). But the body is called a tabernacle, because we dwell in it as in a war against enemies and it remains a short while: ‘The laying away of my tabernacle is at hand’ (2 Pt. 1:14). Therefore, it should not be served.”