Many families have fairly baseless claims to be descended from famous Roman families. Baseless largely because of the length of time and scant records. However there are almost certainly many people descended from prominent Roman families alive today, almost certainly unaware. The noble, and still existing Orsini family lay claim to be descended from the Julio-Claudian Dynasty for instance.

One that I’ve always been fascinated by was Arnulf of Metz, patrilineal grandfather of Pepin of Herstal, who was himself an ancestor of Charlemagne. Arnulf was the descendent of one Tonantius Ferreolus, Roman Prefect of Gaul in the 5th century, and his matrilineal grandfather was Flavius Afranius Syagrius, Roman Consul in the late 4th century. If true, then yes, many modern noble families are directly related to Late Antiquity Roman Aristocracy, as most modern European nobles are descended from Charlemagne.

Whether any of this is factual is uncertain. However, like I said above, there are almost certainly still people descended from the ancient nobility, albeit without knowledge of their ancestry, or without credible records to prove it.