A lot depends on the level of will brought to the renunciation. This same scenario can be applied to anything in life - a gained threshold, a body. What is renounced dies. However, what does the renouncing doesn't die. Death is what happens to a form when the living inhabitant exist or moves on or leaves.
Life can never die.
Life is life. The renouncer, the actor, the being, the Christ in us, is liberated. If one's sense of the real is locked into the physical or material world, there can be no liberation in renunciation, just death. Renunciation is the step necessary for resurrection to happen - no renunciation, no resurrection. Holding on to that which should be let go, needs to be let go, will eventually be let go, regardless of how hard one holds on, leads only to pain.