For the most part, Roman aristocracy outside of the city of Rome had been becoming increasingly insular and isolated well prior to the fifth-century fall of the city (and thus the Empire). As Matthews argues, the after the economic collapse of the third century (particularly in the West) the aristocracy had already begun to retreat to villae and "country" holdings. While those who remained in and around the city of Rome, picked up the power that lay in the streets as the Imperial court moved eastward. By the time of the fifth-century invasion, when Gibbon tells us that the western empire had fallen; most of the actual power and authority in the western empire lay not with the Imperial court, but rather with a burgeoning aristocracy and "new men" who were not from the families that held power for centuries in Rome.

So, once the city and the western empire falls, and the "barbarian" kingdoms coalesce out of the shards of Empire left behind, the Roman aristocracy neither scrambled to adjust, nor bemoaned its new position. These new kingdoms needed politicians, expert men who could run things like... You know... kingdoms. The aristocracy, already holding large amounts of land in many of those new kingdoms, was quick to come to the aid of their new leaders--most of whom had been raised only nominally "barbarians," and were well aware of the talent that an old Roman educated could stoke. As Burns has (beautifully) [shown] (http://books.google.com/books/about/Barbarians_Within_the_Gates_of_Rome.html?id=2ms5CWtIQ5oC), as early as 375, the barbarians who would become the Kings of the post Roman period were a part of Frontier society. They were neither interlopers nor enemies (Burns, xx).

Meanwhile, those aristocrats who weren't so much for the political thing happily faded into the Church, and that's shown in the rise of the ecclesiastical system after say 400ce. As the Empire contracted, beginning around 400, the structures of power and organization left behind in many places outside of the city of Rome (and within too, see below) were religious. Churches, shrines, holy sites, monasteries... All of these were up for grabs as sources for local power as the superstructure of the Empire fell away. Ralph Mathisen did a good job summarizing this process in Gaul (and showing how that led to conflict within Gaul) in his book, which although a getting on in years is a good choice for the subject. The men who became the leaders of the powerhouse monasteries of Arles, Lerins and Marseilles, were the remnants of aristocracy. They were the aristocracy reborn, what aristocracy and elite power and authority would look like once the western empire was dead as a door nail.

Essentially, the aristocracy never went gently into the goodnight of Western imperial collapse. The aristocracy survived, evolved and thrived with new titles, new last names, and under new kings. They continued to have the same undeniable influence over western culture and society after the fifth century because they continued to shape and dictate culture and society from the top down--just as they always had. That the Roman aristocracy was absorbed into the new kingdoms of the Lombards, Merovingians, Franks, Burgundians, Anglo-Saxons, Goths or whatever else is not a mark of its deterioration. It is, rather, a mark of aristocratic resilience and plasticity.

For primary sources on this, a nice early "oh for the good old days..." rant about how the world was ending and no one knew how to be an aristocrat anymore, see Ammianus Marcellinus in his History.

To see how the new barbarian kings understood their new worlds and the place they had for Romans in those courts, see Gregory of Tours' History, which while written later (sixth century) deals largely with the development of the Frankish Kingdom (court and elite culture) after the end of the Western empire.

Further north, the second book of Bede's Historia offers some similar discussion (although, spoiler alert, he's super obsessed with proving the might and right of the Church, and thus he sometimes gets lax in describing secular details).

For a survey-like overview for the entirety of the empire, and an all-round great book, see Peter Brown's [World of Late Antiquity] (http://www.amazon.com/The-World-Late-Antiquity-Civilization/dp/0393958035).

For the view from the east, and another ranty version of how the world was falling apart without the old ways of being an aristocrat, see Emperor Julian's Misopogon. It's not what you asked, but it offers another viewpoint of the same decline and then rebirth of aristocracy as something new and different around the time of the death of the West.

I can definitely think of more, but I have to put a small child to bed. :)

Also, did many of them flee to the eastern empire?

During Justinian's re-conquests were there any old Roman families requesting that their lands to be returned to them?