The same apparent disjunction has been noted for the bronze coins of Caligula: Dio Cassius says that the Senate decreed their withdrawal and destruction, and moreover that this decree was actually carried out, but VESTA asses of Caligula are nevertheless very common today.
Some scholars have therefore doubted Dio's account, suggesting for example that only the government's supply of unissued Caligula bronzes was melted down, with no attempt to withdraw those in actual circulation.
About fifty years ago, however, it was observed that there is evidence to support Dio's assertion. First, Caligulan bronzes are indeed very uncommon in hoards buried and at sites abandoned soon after Claudius' accession. Second, the counterstamp NCAPR is found on most types of sestertii and dupondii of both Tiberius and Claudius, and on the SIGNIS RECEPTIS
dupondii struck by Caligula for Germanicus but without adding his own portrait or name, but virtually never on sestertii and dupondii bearing Caligula's portrait or name: not on his portrait sestertii, not on his Temple of Augustus sestertii, not on his dupondii for Nero and Drusus Caesars bearing Caligula's name on the reverse, nor on his CONSENSV dupondii of Divus Augustus
because they depict Caligula's statue on the reverse. I don't know whether BMC is right to list one exception, which would have to be a mistake: NCAPR on Caligula's sestertii of Agrippina I that call her mother of Caligula. In any case, the conclusion is clear: coins bearing Caligula's portrait or name were not countermarked
either because there were none in circulation at the place or places where the countermark was applied, or because those that were still in circulation were withdrawn and melted down rather than being countermarked
and rereleased into circulation!
What, then, about all those bronzes of Caligula and coins of Domitian in all metals that have survived until today? I think the explanation is actually very simple: it was impossible for the government to come anywhere near withdrawing all of the coins of a particular emperor which had entered circulation and were spread in innumerable examples throughout the empire. I would doubt that any emperor was ever able to withdrawn more than say 25% of the circulating coinage of a condemned predecessor. 75% of it remained in circulation or in hoards, so a lot has been able to survive until today too, and as collectors we hardly notice the difference.
I have never heard of the distinction between abolitio and damnatio memoriae
that David A. reports from Jones, but doubt that is the correct explanation for the case of either Caligula or Domitian.