In Biology, there's the concept of Stochastic Mutation. It's most commonly attributed to viruses, for example HIV is a known stochastic mutator. In these cases, some (not all, just some), types of cell mutations occur, where there's no selection pressure - the virus changes its protein coat in one of several ways (4 for HIV), and type B is just as likely to mutate back to type A or into Type C or D, as to stick where its at. In equilibrium, none of the protein coats is preferred by natural selection, and there's no pressure for one type to come to dominate. HIV also undergoes non-stochastic mutations, just like (we think) everything else with a genetic code does, and stochastic mutation has been studied for many other viruses and probably happens in more complex species.
That's the point - evolution is essentially a two part theory, a synthesis of Mendel's genetics including mutation, and Darwin's natural selection. Cases where all the organisms subject to selection pressure are identical, are not evolution*, and cases where the organisms are not identical but there's no selection pressure applied are not evolution either, and so there really are at least two categories of biological change which are not evolutionary. It's just that 'cases where there's no selection pressure' pretty much discribes some sort of paradise where nothing dies or is limited in how often it reproduces, so there are not a whole lot of known examples of that, especially over a long term, and it would be pretty expensive to create such an environment over a short term.
* If you had some organisms, and they have 0% chance of mutating in the particular way that responds to that particular selection pressure, then you could say that they are identical in that respect. Imagine for example a bunch of Leopards suddenly introduced to an environment where there are abundant fish in deep subsurface pools which can only be reached through narrow fissures. There's really no selection pressure sufficient for those Leopards to start adapting into creatures that can squeeze through six inch wide cracks and use their gills to dive deep enough to catch those tasty fish. All the Leopards are effectively identical, in that they are identically unsuited to take advantage of the new factor in their environment, tasty deep dwelling cave fish. However, I get a feeling you would reject generalizing that sort of example into one of the cases such as you are asking for, so let's just stick to Stochastic Mutation