I think one approach would be; restoring it to a known stable equilibrium. Meaning, if without wolves things continue to deteriorate and clearly hasn't reached a stable equilibrium but you know that with them things were stable over some long term period then you should reintroduce them
That does have the slight disadvantage that a glassed parking lot, utterly uniform and totally devoid of all life, is quite stable.
I agree that it'd be lovely to have a definition that is devoid of subjective (human) judgement, but I don't think "stable" is a useful direction to go for such a definition. It's way too easy to reach stability by ending up at some hellhole ecosystem that is lifeless or exceedingly uniform with nothing interesting. Which, yes, is entirely subjective. That's my point.
Alternative ways to go that seem more suitable to end up at a worthwhile definition that most ought to be happy with:
* Diversity. An ecosystem with more lifeforms is better than less, and complex lifeforms count extra. How much extra is for somebody to write down in detail at some point.
* Utility to humans. An ecological system that constantly causes issues to humans, for example by flooding out a town, spawning plagues that ruin crops, and so on is 'bad'. An ecosystem that humans like spending time in is 'good'.
We are humans and ought to be able to come together and find definitions close enough to what we want without falling into smashing each other's heads in because our definitions of 'nice to walk through' differ slightly. Part of what annoys me about 'modern' political thought is that it presupposes: Everybody hates everybody and we're all infantile morons who are utterly incapable of finding any common ground (and thus only solutions that work despite that state of affairs are worthwhile to think about). This isn't hard to determine. We don't need to eliminate human subjectivity from it.
There is absolutely stability if you zoom out to the time scale that permits evolutionary adaptation (and of course, if you zoom out much farther it all devolves to noise again). But it’s specious to say that “the only constant is change” and then declare all comparisons moot.
I think it’s an elementary definition of stability. Just because the derivative of the function is never zero doesn’t mean it contains no useful information.
