Since the soul, as intimately connected with the Form of Life, cannot admit of death, it must either withdraw or disappear at the approach of death. But if the soul is undying, it cannot possibly disappear and perish. Therefore, it must simply withdraw at the approach of death. Therefore, Socrates concludes, the soul does not die with the body, but simply withdraws from it, living on, eternal and indestructible. At this point, Cebes admits that he is entirely convinced by Socrates' argument.
Plato's fourth and final argument for the immortality of the soul is probably the best and most convincing. Certainly, Plato treats it as such. It is the most direct application of the Theory of Forms to the question of the soul's immortality, and, as Plato constantly reminds us, the Theory of Forms is the most certain of all his theories.
It seems that Plato is asserting here a third metaphysical level in his theory. If we take the example of a beautiful person, not only does Plato want to say that there is the Form of Beauty and there is the beautiful person, but he also seems to say that there is the beauty present in that person which is distinct both from the person and from the Form. This beauty can come and go, and must, for instance, either withdraw or disappear at the approach of ugliness. This might lend some credence to the view of Forms as stuffs: there is a little bit of beauty in each person, which comes and goes as it pleases.
Plato also asserts here the existence of essential properties. (This idea will bear far more weight in Aristotle, but it does play an important role in this argument.) The distinction is drawn between essential properties, properties without which the thing that has them would be other than it is, and accidental properties, properties that just happen to hold of a thing, but which it could do without. So, for instance, being orange is an accidental property of fire, whereas being hot is an essential property. A fire can become blue, for instance, and still be fire, but a fire cannot be fire unless it is hot: there is no such thing as a cold fire.
Analogously, Plato suggests that life is an essential property of the soul, whereas its existence within a body is only an accidental property. So a soul can leave the body and still be a soul, but it cannot be a soul unless it is alive. Further, because it cannot possibly admit of death, the opposite of life, a soul cannot die. We should note that there is a difference between being destroyed and dying, but both of these options are ruled out for the soul. Pre-Socratic physics held that nothing could cease to be without being replaced by something else, so absolute destruction is not possible. The living soul cannot simply be destroyed, but would at the least be replaced by something else--namely, death. But since the soul's essential property rules out this possibility as well, it must live on forever.