So I'm gonna do the thing I always do here and not answer your question but instead explain why your assumptions are wrong and why your question isn't valid. Much of the vestiges of the Roman empire remain today whether it be the motto of Rome itself which remains Senatus Populesque Romanus, various Senates, through out the world, or the fact that almost 700,000,000 people speak derivatives of Latin today in places the Romans didn't even know existed at the time.

Roman culture very much survived after its fall (whether you place that date in 476 with the fall of the west or 1453 with the fall of Constantinople). The first point I want to bring up is that the subjects of the Roman empire didn't necessarily know that the empire was falling when it "fell" because people didn't have the same concept of a nation-state that we do today. In many of the western provinces Roman traditions carried on even as "barbarian" came to rule. In Gaul the Franks more-or-less assumed control of the area (giving it its modern name; France) but Latin remained the Lingua Franca. Former roman titles and areas of administration remained. Duke ccomes from the Latin Dux meaning leader; Count comes from the Latin comitem meaning companion. Barbarian leaders took the names and positions of what had previously been position held by roman authorities and these men may well have conceived of themselves as continuing that tradition given that many of them had lived under Roman rule for their entire lives. 350 years after its fall the in the west the Roman Empire still had so much cultural influence that when Charlemagne(which is francophone version of Carlus Magnus, Charles the great in Latin) carved his empire they called it the Roman Empire In Romano-Britain central Roman authority left the island in the 4th century but the inhabitants continued to live as Romans and considered themselves to be a part of the empire despite the fact that the empire exerted no control over them. It wasn't until the Saxons, Angles, and Jutes arrived that this began to change.

This just barely scratches the surface of what the Romans left behind what influence they had going forward from the fall of their empire. The Roman state existed for 1000 years in the west and exist for over 2000 years consecutively from the Founding of the City to the fall of Constantinople and they had long and far reaching effects. hell this post is typed in the very same alphabet they popularized (with some slight modifications)!