I'm pretty sure they would get destroyed, but people have argued that they stay on the field negated, since the card does not explicitly state "the card gets destroyed and sent to the graveyard."
In my defense I state that it makes no sense that a card never be activated (since LaDD prevents activations) and still remain face up on the field.
They respond that since it never got activated it gets set again, and therefore they think they can get away with activating it every turn to weaken my LaDD.
I'm looking for hard evidence that I can show these kids the next time we have this comes up.