It can be argued that the Roman empire didn't truly end until WWI in 1918, 106 years ago.
The fall of the Byzantine Empire (aka the Eastern Roman Empire) resulted in a number of subdivided but diplomatically aligned states. By the end of the 19th century a number of European powers were still vying for some claim to the lineage of the Roman Empire (and the Emperor title). But as consequence of the war, the German/Prussian, Austro-Hungarian and Ottoman empires we're all dismantled (and France was out or the running because of the revolution) so every entity with a claim was dead or out of power for the first time since the 11th century.
I'm not a historian but can there still be an empire if there's no emperor or empress? The Eastern Roman empire is a misnomer for the Byzantine Empire, which started when the last Roman emperor, Romulus Augustulus, was deposed in the 400s by some Germanic warlord whose name I forget. How is that not the end of the Roman Empire? Seems like deciding to call Ukraine Western Russia.
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.
At the point the western half of the Roman Empire collapsed they were using a system with two emperors due to the massive amount of territory being impractical for one man to govern, senate or no. Only one of the imperial titles imploded, with the other going along just fine for centuries before that part of the empire also started to collapse.