In the recent novel HALO: Silentium, it was revealed that
The Forerunners rose up and exterminated the Precursors, but they were so ashamed that the assault force relinquished their weapons and stayed on Path Kethona (another galaxy, to us the Large Magellanic Cloud)
Also, at the end of Silentium, the Librarian is on Earth, creating the Portal discovered in HALO 3, but
she may have survived, as she appears to be talking after the effects reach Earth.
According to 343 Guilty Spark, at least the The Librarian is alive, and he knows where to find her. It has been said that the remaining Forerunners made an exodus out of the Milky Way Galaxy to which no one knows their current fate.
Somehow the Didact survived the Halo firing, though whether that was because he was in his Cryptum or because Requiem was similar to a Shield World, or for some other reason we don't know.
So what happened to these Forerunners? Were some of them out of range of the Halo Array when they fired? Is it possible that some were somehow able to shield themselves from its effects?