Or did they die out and retired to Rome?
I often read things as that the conquering barbarians mixed with local Roman nobles, creating the noble families of the Middle Age. Of course, many family lines died, and many more were created from humble origins (condottieros, small gentry getting its way up the hierarchy) so I wondered if there are genetic studies linking surviving noble families to some Roman traits. If this definition makes any sense.
We like to read continuity in history, even through transformations, I wondered if it was time for me to change this view.
There's been some recent research, reported (here) [http://www.telegraph.co.uk/science/science-news/9888402/One-million-Brits-descended-from-Romans.html]
The answer is really a quick one, so sorry for not having more citations.
There are also genealogical records of peerage in Britain that make the same claim; the genetic research supports those claims. So the answer to the second question (noble families and Romans) is a qualified "yes," based on older genealogical records.
I'm not sure who the "conquering barbarians" are in your question (I guess you're taking a Roman point of view on barbarians? But I can't tell what time period you intend to indicate for "conquering" barbarians).
The study quoted above did not specifically study nobles. It was male line (Y chromosome) research.