IMHO, an "invariant" is only relative to the current system to be build, based on a specific set of specifications. As soon as you build a new version of the system (either because you change the functionalities, the implementation or because the environment change), you're expected to check which invariant still applies and which should be added, removed or changed...

In a way, "invariant" are the same as "tests sets": they are here to help to ensure that the product will have some specific properties. Both are used during the product development and checked. And both must be updated when the specs change