How really certain are we that the Ancients were destroyed completely? Maybe they had some common sense and collapsed a node behind them, sealing themselves off from the Shivans in a system the Shivans wouldn't think of looking.
If that happened, they could begin their own civilization again, isolated, but alive. Maybe that's what the Lucifer fleet of FS 1 was looking for? The Shivan rulers went, "Hey, we think some got away, but we sure as hell are gonna get those bastards..." and they sent the Lucifer and a small fleet because they thought not many Ancients survived, therefore, they couldn't put up a fight.
Secondly, just how much space did the Ancients rule? I know that it was said that some of the Vasudan space was once in Ancient territory, but perhaps the Ancients' systems stretched past Gamma Draconis? I mean, since they said they wiped out a bunch of simpler civilizations in the various cutscenes, what stopped them from wiping out early humans and vasudans?