A Ghost cannot improve her Morality, and is doomed to unconsciously watch it slip slowly away over the years. Such poor creatures may end up Damned before they even know the meaning of the word.
Wraiths, on the other hand, are able to maintain, and even improve, their Morality as time goes by. However, the ravening voice inside their heads can grow more powerful in that time as well. And the more powerful the Shadow becomes, the less a Wraith is able to raise her Morality above a certain point; A Shadow can even force a Wraith's Morality to go down a notch, if it gains enough power to overwhelm it.
The basic rule is that the extent of the Shadow's power forms an upper limit to how Moral a Wraith can be. For example, a Shadow with an Angst of 3 would keep a Wraith from ever improving her Morality past a 7. And if that Shadow's Angst grew to 4, the Wraith's Morality would be shoved back down to 6.
Wraiths mostly follow the Morality rules on pp. 91 - 94 of The World of Darkness, with the following exceptions:
 * Wraiths do not get Derangements, and any Derangements that were had at the time of death are folded inwards, to become quirks of the Wraith and aspects of the Shadow. {An exception to this rule are those who died from Insanity, as they begin play with a "mild Derangement." This cannot be healed, but it cannot get any worse, either}
* When a Wraith loses a Degeneration Roll, she loses a point of Morality as normal. Should the Wraith then lose the roll to check if she suffers a mental imbalance because of the experience, the Shadow gains a Tainted Essence-free shot at a Harrowing, just to see if it can gain a dot of Angst in the mental confusion that follows. {See "Harrowings," in the Chapter on Shadows, for more information}
 * A Wraith can, with Storyteller permission, add a Modifier to her Degeneration Roll if she acts in pursuit of her Virtue unless her Shadow type is connected to her Virtue. If that's the case, then she cannot add a Modifier, even if the situation would otherwise merit one.