By the power of truth, I, while living, have conquered the universe.
Posted by: That Doom Guy
exactly what they said about the forerunners..... Didact
~Doom Guy
No, there has never been any reliable statement in the entire Halo series telling us that all the Forerunners are dead - it's simply a preconception based on second-hand accounts and unreliable narrators.
Certainly many would have perished since not all of them would have made it to the various Shield Worlds, as 343 Guilty Spark said in Halo 2:
"They, and all additional sentient life within 3 radii of the galactic centre died, as planned."
But in Halo 3's last terminal, it's revealed that they are, in fact, alive, and have gone on the Great Journey. The librarian confirms this in Halo 4's campaign where she says "the Forerunners made plans for a final Great Journey".