Who would that be, not Romulus Augustus, that little pretender? The last western Emperor was murdered (Julius Nepos, Emperor 475-480, he was recognized by the East, and Odovakar minted coins in his name), and the last eastern Emperor died in battle.
On when Rome was doomed, after it and the rest of the little Balkan states failed to really do something against the extremely weakened Ottomans after they had been smashed by Timur at Ankara. If the Balkan states had worked together it would not have been impossible (though obviously difficult) for them to drive the Ottomans from Europe.
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