2 Because then this Psalm is singing of the Passion of the Lord, see what is the title that it has: “at the end.” The end is Christ. Why has He been called end? Not as one that consumes, but one that consummates.
3. “At the end, corrupt not, for David himself, for the inscription of the title; when he fled from the face of Saul into a cavern.” We referring to holy Scripture, do find indeed how holy David, that king of Israel, from whom too the Psalter of David has received the name thereof, had suffered for persecutor Saul the king of his own people, as many of you know that have either read or have heard the Scriptures. King David had then for persecutor Saul: and whereas the one was most gentle, the other most ferocious: the one mild, the other envious; the one patient, the other cruel; the one beneficent, the other ungrateful: he endured him with so much mildness, that when he had gotten him into his hands him he touched not, hurt not....What reference has this to Christ? If all things which then were being done, were figures of things future, we find there Christ, and by far in the greatest degree. For this, “corrupt not for the inscription of the title,” I see not how it belongs to that David. For not any “title” was inscribed over David himself which Saul would “corrupt.” But we see in the Passion of the Lord that there had been written a title, “King of the Jews:” in order that this title might put to the blush these very men, seeing that from their King they withheld not their hands. For in them Saul was, in Christ David was. For Christ, as says the Apostolic Gospel, is, as we know, as we confess, of the seed of David after the flesh; for after the Godhead He is above David, above all men, above heaven and earth, above angels, above all things visible and invisible....And because already it had been sung through the Holy Spirit, “Unto the end, corrupt not, for the inscription of the title:” Pilate answered them, “What I have written, I have written:” why do ye suggest to me falsehood? I corrupt not truth.
Source: The Enarrations, or Expositions, on the Psalms (New Advent)