It's also possible for a creature to lose a Destroyed: ability in the process of resolving Destroyed: abilities, but it is not possible for a creature to gain a Destroyed: ability after it has been tagged for destruction.
For example, Say the the active player has Curia Saurus in their play area and int their battleline they have Praefectus Ludo as well as a creature with 1 Æmber on it. When the latter creature is tagged for destruction, it has 2 Destroyed: abilities:
If the active player resolves the Destroyed: ability granted by Praefectus Ludo first, the creature will lose the ability granted by Curia Saurus, as it no longer meets the requirement to have the ability. If some other effect moved an Æmber back to the creature, the creature would not regain the Destroyed: ability granted by Curia Saurus.