Based on the fact that Alivia somehow has to "help" Rand to die.

Why exactly Alivia? She is a powerful battle damane, and it's pointed out in KoD that she can pick up new weaves very quickly. We know that Rand apparently already began to discuss the matter of that Prophecy with Alivia.

I think eventually Rand will realize that he has to fake his death to trick the Shadow and operate against it unseen (Logain will basically take Rand's place). Possibly Moiraine's return from the "dead" or the knowledge that the Forsaken are reborn with new identities will even inspire this plan. Maybe Alivia will remember and figure put then the Seanchan stasis weave for humans or she will yet pick the weave up from other Seanchan damane during a battle.

As said, I think in really dire cases a Seanchan might allow that a weave is basically put around his body to keep him alive till he gets medical aid, because it wouldn't be a "surgical intervention" like Healing, which really affects the interior of a body.

Thus would explain all the Prophecies about Rand being dead but alive and why Alivia is important.