Why Nagini died even though it was a horcrux?

Nagini and Harry were the two alive horcruxes that Voldemort created.

When he tried to kill Harry, he accidently killed his own piece of soul. So that means when someone try and kill the living creature holding a horcrux then it kills horcrux and not that original living creature.

If the same logic we apply for Nagini , the second living creature holding a horcrux.Then it should not die.But when Neville try to kill Nagini , both died.

Can anyone explain why?

Edit : So it removes both souls from the body if it's physical.Then how the Avada spell knows which Soul has to be removed when casted?