Plato's Republic famously describes the decay of the regimes, a process by which a society decays from the best regime, that of aristocracy, to the lowest, that of tyranny. However, the purpose of this concept of regimes is to expand upon Plato's extensive analogy of the city; he uses his "city in speech" to explain the concept of the soul (the analogy is created in section 368, Stephanus Pagination), and every regime has an analogous soul. For example, the regime of an oligarchy is analogous to a soul that values wealth over all else, and thus abandons justice.
One of the most important principles of his city in speech is as follows:
For everything that has come into being there is decay, not even a composition such as [the aristocratic city] will remain for all time. (546a)
Thus, Plato sees it as axiomatic that every regime will always decay into the next. By extension, therefore, every soul is constantly decaying. However, as with the regime, the soul too must decay to a state of tyranny; in this state, the soul has become enslaved to the beast of its desires (one of Plato's Tripartite of the Soul), and is very unhappy. As he says, the aristocrat is 729 times happier than the tyrant (587e).
However, (as far as I know) Plato does not at all suggest any way out of tyranny. It's as if the regimes are decaying constantly until they hit rock bottom—tyranny—and then there's nothing to be done; the soul or city is stuck in the horrid state of tyranny for eternity.
Now, this just doesn't seem to match the rest of Plato. If anything, he would be sure to provide a path of escape for anyone or any regime, because he wants people to be just. Much of The Republic is dedicated to arguing that the just man is happier than the unjust (the argument having begun with the Myth of Gyges), with the purpose of motivating people to act justly.
Therefore, it seems to me that even the soul of the tyrant should have a chance to recover (anti-decay?) back up the chain of regimes, so that it can be just once more. Either that, or Plato determines it to be a kind of eternal hell for those who are too careless and allow their souls to decay too quickly.
So, does Plato see tyranny as the final and permanent stage of decay, from which there is no escape? If so, does that mean he believes that older people and societies must gradually become more corrupt? If not, how does he allow for the soul not to decay, or to escape from tyranny? Perhaps here is where the city in speech breaks down as an analogy for the soul?