Histories of Valyria, Volume 11
While the Targaryens are commonly believed to be the only Dragonlord family to escape the Doom of Valyria, they was in fact one other family to survive. The Vallarama Family left Valyria 9 years after the Targaryens, 3 years before the Doom.
At the time that they fled, the family only consisted of Lady Behra and her three daughters: Saenenya, Naeremera, and Draenesella. It is believed that Lady Bahra and Lady Daenys were good friends and that Lady Bahra trusted Daenys' warning about the Doom. However, Lady Behra's brother-husband, Lord Maehavar thought the dreams folly. It wasn't until after his death that Lady Bahra fled the city with their dragons.
There is evidence that the family spent some time on Dragonstone, before leaving in 103 BC to find their own place. Some reports from maester at the time tell us that the Vallarama family went to the western edge of Westeros. They stopped in between cities before continuing off the edge of Westeros.
There has been no mention or sighting of the family since then, and it is believed that they died out in the seas trying to find land.
It is worth mentioning that the Vallarama family was the three Elder Dragononlord family of Valyria. They had been a ruling family of Valyria for nearly 3,000 years prior to the Doom.
