When called by the Horn, the heroes do not exist in the flesh (as they would be upon rebirth for example). They cannot be touched by the one-power, and there is every reason to believe they cannot be harmed by physical means. They are like indistructible ghosts for the most part.

Remember Birgitte's words: "As for Falme, the Horn had called us; we were not there as you were, in the flesh. That is why the power could not touch us."

We don't have a lot of knowledge about how the return once their duty is finished, but from what we do know, they simply vanished at some point after the battle of Falme. Nothing physical is left behind.