If he's been gaping alot and you see stringy saliva when he is doing this, it is possible he has an URI (upper respitory infection). But that picture isn't good enough for me to be able to tell what it is. Deep breaths with an open mouth on a regular basis is not good. Someone else may have more info.
Is it still there? Could he have eaten a fake leaf or something and that is the stem of the plant? It is hard to tell from your pic what it is, but does not look like saliva to me. It looks too stiff.