Are you referring to when Ventus fell into a coma after Xehanort removed a piece of his heart and sent him to Destiny Islands to die “in peace”, or when he fell into a coma again after the final battle with Vanitas?
If it is the first one: After Xehanort extracted Ven's heart (from which Vanitas took too much of), Vanitas was perfectly fine, whereas Ventus was left to die. Thankfully, newborn Sora saved him.
“But Vanitas took too much of Ventus's heart, and from that fracture, I could see the last of Ventus's light was slipping away.”— Xehanort’s report 10
But, if it is the latter: Ven nearly died, not because Vanitas died, but because of the destruction of the X-blade damaged his heart.
“The χ-blade is made of your heart, too, idiot. If you destroy it, your heart will vanish forever” — Vanitas
In other words, Ventus and Vanitas are completely independent from one another. They were once whole, but no longer are.
If Ventus dies, it has no effect on Vanitas, and if Vanitas dies, it has no effect on Ventus.