Most historians (minus a few holdouts, like Peter Heather) generally agree there weren't barbarian invasions in the fifth century. What we have instead is a complicated series of civil wars and internal instabilities resulting from power struggles by Roman generals - some of whom were of barbarian origin - to put themselves on the throne. But none of them were successful enough to take control of the whole empire, and these civil wars ultimately resulted in fragmenting the empire into smaller kingdoms.

Because everyone's goal was to get control of at least part of the empire for themselves, there wasn't an attempt to wipe out Roman buildings or culture. In fact, some groups like the Ostrogoths settled easily into the urban infrastructure of Italy and maintained the status quo with few differences (until Justinian, the eastern Roman empire, invaded Italy and destroyed a bunch of cities in the 6th century). Barbarian administration was handled in Latin, cities still show evidence of an educated latin-literate elite (you can trace this by the inscriptions they left behind on monumental architecture), and it's very difficult to see a simple picture of decline or de-Romanization that we can point to and say: that is where the barbarians killed civilization (contrary to what Bryan Ward-Perkins argues).

That said, the Mediterranean world underwent significant changes during late antiquity, and these changes did result in deurbanization in many parts of the (former) Roman empire. Chris Wickham characterizes this period as a time of regionalization during which trade networks contract and local economies become more self-reliant. One consequence of this regionalization is that some areas see a decline in urbanism; both in others, urban populations simply shifted as new cities became more important (eg Rome's population collapsed, but the Italian city of Ravena grew to its largest size under its Ostrogothic rulers).

These changes in the urban landscape had begun before the fifth century, and were part of a long transformation of centers of power and, more importantly, elite spending habits. Roman civic architecture was incredibly expensive to build and to maintain, and the monumental buildings in the empire's cities depended upon continuing donations from wealthy elites. By the late fourth century, the burden of maintaining civic infrastructure was becoming more expensive than many elites were willing to spend, and more and more diverted their resources to other forms of ostentatious investment like building large country villas or, increasingly, donating their wealth to the church instead of the city. As money for urban architecture dried up, some cities chose to ignore or, sometimes, to tear down the crumbling buildings that no one wanted to maintain. In some cases, the decision to destroy a crumbling edifice was a sign of continuing urban vitality: the spaces were sometimes turned into park lands, or filled with vibrant commercial stalls and marketplaces. In other cases, people decided to move out of the crumbling cities and looked for homes elsewhere - the city didn't have as much to offer as it had before, when empire-wide trade was at its height. As regional economies became more important, the road to success became increasingly connected (in many - but certainly not all - parts of the former empire) with managing local production instead of participating in an empire-wide urban culture.

In regions like Britain, which was far from the thriving metropolis of Ostrogothic Ravena or Roman Constantinople and Alexandria, cities disappeared in the fifth century, and the whole population became rural and agrarian. In northern France, a similar process of deurbanization left some cities, like Metz, empty for several generations before they were resettled and revived. In southern France, however, cities remained an important part of daily life throughout the early middle ages, and Italian archaeologists are becoming increasingly aware of a continuing vitality in urban life in Italy after 476. North Africa's cities were destroyed not by the Vandals, but by Justinian in the 6th century, but the region continued to have a more restricted urban culture under Byzantine rule which was not ended by the Muslim conquest. Spain maintained many urban centers, and had a productive economy which continued to prosper under the new Visigothic kings.

So on the whole, the picture is complicated. The barbarian generals who sought, and failed, to become new emperors didn't end urban life in the western empire. The century before and after the establishment of their kingdoms did witness many changes in the urban fabric of the western Mediterranean, however, and many regions did grow more isolated and saw their cities shrink or, in some cases, entirely disappear. In others, urban life moved and changed, but continued to be an important part of people's lives. Rather than there being a single, simple narrative of decline and fall, it's become clear that each region has its own story of economic and urban continuity or change.

I'll attack this question from another angle.

Not to be overly facetious here, but the question of "last true Roman citizens" has roughly the same problematic connotations as the "no true Scotsman" fallacy, in that it's quite an arbitrary and potential ever shifting series of definitions.

What it meant to be a "Roman" in the 5th century was worlds different from what it meant in the 3rd and 1st.

In the 1st century, being Roman was synonymous with the very coveted status of "Roman citizen" which carried with it a particular set of rights and privileges that went beyond simply being a denizen under the authority of the Roman Empire. It also embodied a set of cultural and literary expectations that we actually associate now with being a Roman citizen. And because not everyone was a Roman citizen, it made that status more powerful.

In the 3rd century, thanks to the edict of Caracalla, being a Roman simply meant being a "tax-payer" because he wanted to expand the financial base, and thus liabilities of individuals in the empire, and the "status" of Roman citizen lost a lot of its cachet. Of course it was also the 3rd century, because of both the crisis and the reforms of Diocletian, who began setting up alternate capitals throughout the empire where the idea of a Roman Empire shifted away from being seen as simply the commanderie of the city of Rome to that which was under the authority of the emperor wherever he was, and also simultaneously "the civilized world."

By the 5th century, "Roman" in the west was associated with what's left of the military, which frequently was mostly barbarian in composition, and what was left of the administration. And thanks to the two sacks of Rome, as well as Augustine's writings on the subject, Christians weren't quite sure how to place their identity within this "Roman" world, and while they might see themselves as denizens of the "Roman Empire", they might not see themselves specifically as primarily "Romans" even though they were legally regarded as such.

By the 7th century, with the fall of the empire in the west, the identity of "Roman" really only extended to two particular areas of western europe. People still considered themselves (or at least other people considered) the non-Frankish aristocracy of southern France as "Romans", as well as those living in the area around Ravenna under the control of the Byzantines, which survives in some form as the region name of Italy of "Romagna." But by the 7th century, "Roman" as an identity no longer embodied any of the concepts of a 1st century Roman. It was at best, primarily a regional identity, i.e. "you were a Roman because you lived in the land of what used to be controlled by the Romans", secondarily maybe a class identity "you are an aristocrat in the land of what used to be controlled by the Romans", third (not inclusive) a legal identity "we allow you to settle your cases by Roman law rather than Germanic law."

By the 9th century, the time of Charlemagne, "Roman" was pretty much stricken from the identities of everyone in the west. Even when Charlemagne was crowned "Emperor", though Leo wanted to give him the title of "Emperor of the Romans", Charlemagne actually went with the title "Emperor Governing the Romans", because he wanted to respect the understanding that the eastern empire was where the Romans still were, although perjoratively referred to as "the greeks" by the germanic successor states to the western empire. And even then, the denizens as well as the leaders of this new Frankish Roman Empire did not consider their own identity as "Roman." Their reference point to what "Roman" was, at that point was purely geographical, i.e. "whatever used to be under the extent of the Roman Empire of old." Which as similar to the 7th century conception, was a far cry from the toga wearing Vergil quoter of the 1st and 2nd century.

tl;dr - when the last true Roman lived depends on how you define Roman.

PS - Technically, true Romans continue to exist. They're in Rome.