You're incorrect here again. Byzantium retained its integrity, but Rome, the city, did collapse thanks to invasions by Germanic tribes and the Huns. So did most of Europe that was under Roman control, and some portions of North Africa as well. Constantinople stayed standing for quite a while. Control shifted around, falling into the hands of the Mamluks, Seljuks, and subsequently the Ottoman Turks, from where Turkey gets its name.

There are numerous other civilizations (for instance, dynastic China) that have suffered decline rather than outright collapse. Rome was not one of them though; the entire Western Empire broke apart. It's just not a good example.