I hear the sentence from the song『星のかがやきよ ZARD』
I think there are 2 ways to interpret it:
- I only want you to remain unchanged. (The person whom I want to remain unchanged is only you.)
- I want that only you remain unchanged. (I want that the person who remain unchanged is only you).
There is slight difference between them. In 1, "only" is associated with "want", which indicates: maybe other people will change, but I don't care.
However, in 2, "only" is associated with to "remain unchanged", which indicates: I want you remain unchanged and I want others to change.
That's to say, whether だけ in the sentence is associated with 欲しい or 変わらない will lead to different interpretations.
Considering the context, I think the first interpretion is correct. But does the second also make sence if we only consider the meaning of the single sentence?