I had the problem just the other day, where a Titan attacked and was encaged.
I had the cage moved to my Goblin Zoo, and decided to set up some flood gates to block the entrance and eventually open the cage doors and see if they'd fight, maybe throw in a few soldiers to get experience.
For whatever reason, my proficient animal caretaker decided to lug the Titan a few Z levels up to a main hallway, and then managed to transfer the creature into an Artifact Cage I had.
In moving the cage back, the Titan Escaped! And he beat the snot out of the countess, the animal caretaker (who died soon after when everyone ignored him; the countess was dropped into a tiny bedroom instead of her regular bedroom). War dogs descended on him in a tight corner, and a wrestler finally took him down.
(Titan's give 100 bolts, at least mine did, not bad!)
So I am wondering if they decided it would be great to show off this prized megabeast in an artifact cage? It sure caused chaos.
Of course, at this time, the human and elven dignitaries showed up and sat next to comatose countess for a long time before leaving disappointed. She finally woke up and was miserable, dehydrated, and starving, and dragged herself to the dining hall. While she was unconcious her baby drowned somehow, and I never got around to building the consort's bedroom, so he was tantruming.
At the dining hall, she died of starvation. Within 30 seconds a migrant wave came in and I got a new count and count consort. What a pain!