Part of the ongoing Verse Quick Reference project.

Heb 1:11 THEY WILL PERISH, BUT YOU REMAIN; AND THEY WILL ALL GROW OLD LIKE A GARMENT;
Heb 1:12 LIKE A CLOAK YOU WILL FOLD THEM UP, AND THEY WILL BE CHANGED. BUT YOU ARE THE SAME, AND YOUR YEARS WILL NOT FAIL.”

Hebrews 1:11-12 is a quote from Psalms 102:26:

Psa 102:24 “O my God,” I say, “take me not away in the midst of my days— you whose years endure throughout all generations!”
Psa 102:25 Of old you laid the foundation of the earth, and the heavens are the work of your hands.
Psa 102:26 They will perish, but you will remain; they will all wear out like a garment. You will change them like a robe, and they will pass away,
Psa 102:27 but you are the same, and your years have no end.

Louis Berkhof uses both these verses for a prooftext on immutability:

The Immutability of God is a necessary concomitant of His aseity. It is that perfection of God by which He is devoid of all change, not only in His Being, but also in His perfections, and in His purposes and promises. In virtue of this attribute He is exalted above all becoming, and is free from all accession or diminution and from all growth or decay in His Being or perfections. His knowledge and plans, His moral principles and volitions remain forever the same. Even reason teaches us that no change is possible in God, since a change is either for better or for worse. But in God, as the absolute Perfection, improvement and deterioration are both equally impossible. This immutability of God is clearly taught in such passages of Scripture as Ex. 3: 14; Ps. 102: 26-28; Isa. 41: 4; 48: 12; Mal. 3: 6; Rom. 1: 23; Heb. 1: 11,12; Jas. 1: 17.

Berkhof, Louis. Systematic Theology (Kindle Locations 1181-1184). . Kindle Edition.

Berkhof claims that these verses are speaking about God being unchanging in the sense that any change to God in any respect must be a change for the worse. He is reading Perfect Being immutability into these fairly straightforward texts about God never aging or growing weak.

In the context of Psalms 102:25-27, God is being praised for His everlastingness, contrasted to the short time that people live. The people will die but God will live forever. The narrator contrasts God with man. He points out God’s years are “through all generations”. Those who are changed, die with old age. God is not subject to this same aging.

The broader context is a cry for God to listen to the petitioner’s prayer. In verse 1, there is a call for God to “hear my prayer” and in verse two to “do not hide your face from me”. God is said to watch man from heaven (v19). The petitioner begs for God’s salvation. These are not actions of someone thinking in terms of perfect immutability, in which God does not listen or respond or experience duration. These are the prayers of an Open Theist begging God to listen and act.

The context of Hebrews 1:11-12 is the Messiah sitting next to Yahweh on His throne, in heaven and having a conversation. These facts are antithetical to the Perfect Being narrative, in which God is perfectly simple, timeless, immutability, and cannot be related to anything in any manner. By having relations with other things, this causes change. Furthermore, Hebrews 1:11-12 is applied to Jesus, who lived, died, and rose again. These are all changes, and not compatible with the immutability narrative.

The “You are the same, And Your years will have no end” in both Hebrews 1:11-12 is best seen as one in which God will never grow old and die. Instead, Yahweh (and Jesus) live forever without aging. This is not a prooftext for immutability, but a prooftext to God’s everlastingness and uninterrupted reign.