In fact, even during its heyday, the Roman Empire defied defied definitions. Were you Latin? Roman? A citizen? These and other terms all meant different things as the civilization progressed. There was almost a determined effort to keep shifting definitions around such that the Roman Empire never died. In fact, IIRC, there's a 60 Minutes segment where they interview some Greek monks living on an island. The flag they're flying? The flag of the Byzantine Empire, of course. (Also, the word "byzantine" is mostly our own invention. They considered themselves thoroughly Roman)
Having said all of that, it's completely obvious to any outside observer that major changes occurred, many of which had a negative impact on the population. So something happened. Until one starts in with definitions of what exactly constitutes a valid OEM part for our Theseusian ship and what doesn't, folks are free to completely ignore the discussion, no matter how bad things get.