I think the best example is the PlayStation 2 being discontinued in 2013, as well the PlayStation 1 in 2006
The Byzantine Empire was the Eastern Roman empire - we really on refer to them differently for temporal convenience. The west were the Latin speakers and the east were the Greek speakers (as least for the first half-millennium). And many people still called themselves Emperor of Rome, in a continuous succession, after the fall of the west. For quite a while one of the Pope’s titles was (legitimately) Emperor of the Holy Roman Empire.
By the 20th century it was down to 3 rightful heirs, all trying to make Europe recognize them as THE Emperor. But in the mean time their empires still recognized them as such.
Which claimants are you thinking of? I know the Ottoman Empire and the Russian Empire both claimed to be continuations of the Roman Empire. I don’t think Italy ever claimed to be the new Rome, somewhat ironically, and I think Germany and France had stopped claiming to be Rome as well.
The House of Hohenzollern in Germany. The Habsburgs formally gave up their claim in order to create the Austro-Hungarian alliance/Empire, but they had asserted it less than a generation prior and also claimed their Empire status on that back of it. And in the Ottoman Empire the lineage of Mehmed, including Mehmed V during WWI, claimed to be the continuation of the Byzantine / Eastern Roman Empire.