The remains of the Hunnic Empire limp east into the Crimea, where they drive out the Goths and hole up in the mountains. They're able to survive first the various waves of Steppe Empires from the north by simply not living on the plains, and the Rhomans don't bother with them beyond dumping a few political exiles on them every so often. The Ottomans force them to pay tribute, but they are otherwise left alone. They manage to survive the Crimean Wars by acting as a neutral state, being subjugated into the USSR but coming out the other side still intact, but with many of the social problems of OTL Eastern Europe. To this day, the Khaganate of Hunnia persists as an impoverished and corrupt state, where upwards of a third of the population are alcoholics or drugies, and a third of all children born has FAS.
However, as the sea levels rise, for the first time since the Catalunian Plains, things are looking up for Hunnia. When the ocean overwhelms Southern Ukraine, it will leave Hunnia as an island, and one of the few island nations with enough farmland to sustain itself.
The future of the Black Sea is in the hands of the heirs of Attila.