[member="Eddie"] [member="Nulmak Volora"] [member="Alexander Hark"]
A large majority of the Purebloods did die out during the Old Republic Era, I think due to either a lot of racial mixing or the fact that the Sith were pretty much killing each other off.
However, there are quite a few ways as to how they could have survived to this day:
1)Stasis, though that seems to be everyone's favourite thing nowadays xD
2)Be a ghost like yours truly (died during the First Battle of Bothawui)
3)Longevity; A healthy Pureblood can actually live for about...300 years I think? Minus external factors. There are also a few cases where the Sith have used alchemy and sorcery to prolong their lives, though this usually comes at a great cost (see: the Emperor during Revan's time, Lord Scourge, and maybe Darth Nyriss; They were all in the book The Old Republic: Revan)
4) A lost colony of Purebloods, either in Wild Space or the Unknown Regions, similar to the Lost Tribe in the Fate of the Jedi series.
Just a few helper thingies, if y'all want them.