Jisho

The negative of 変わる, as with any negative, maybe also be an adjective.

See:

変わらない人 (present)
変わらなかった人 (past)
悪い (present)
悪かった (past)

I think I need to clarify what it is I'm actually trying to ask here... The dictionary says it can be inflected as 変わらなくない. Is that double negative a valid usage? Or would it be like saying "ununchanging" in English?

It would be valid, though if you're just trying to say something changes you would just use the normal dictionary form. There are, however, two common cases I can think of where this double negative is used: trying to skirt around having to afirm the positive, or when using negative questions with something that's already the negative.

The first one is sort of like:
A "So, does it change?"
B "Well, it doesn't NOT change..."
But I can't really think of this being used with this verb in specficic. It's more often used with someone trying to not say straight away they're interested in something, or trying to avoid saying something that might hurt the listener's feelings, that sort of thing. For example (in a casual conversation):
A 「まあ、別に行きたくないけど、行きたくなくもない。」[Well, I don't particularly want to go, but I guess I'm not against going, either]

The second is when doing negative questions (just like in English, when one asks "Isn't that strange?" or "Aren't you coming?")
I can imagine this being used with the negative of the te-iru of 変わる like:
A 「あのさ、これ変わってなくない？」
Translating straight up would give us "hey, hasn't this not changed?", but it would be more appropriate to translate it as "hey, this hasn't changed, has it?" or "hey, this one is still the same, isn't it?". (Potentially, this sentence may also be using 変わる in the "strange/different" meaning, context would be needed to decide) If one just asked 「これ変わってない？」 it would be asking for confirmation that something HAS changed.

Both of these in theory can be done with anything in the negative, and they're not rare usage either, especially not the second type.

By the way, if you're looking to say something is "inconstant" or "always changing", consider things like 変わりやすい or 不定