In the game I'm currently playing:

• If I get the sovereign to capitulate; I get him/her to control. He/she has all enchantments at the time of capitulation still active, and I don't have to pay upkeep on them. They all have that 'beaten' weakness, giving -25% accuracy.
• If the sovereign surrenders out of spite, I get what you see. He/she just stands there and you can do nothing about it.
• If the sovereign is wiped out...he's gone. Guess that's the only time those yoyos actually die. Personally, I'd like to control them in this instance aswell, though they should have a different weakness placed upon them than if they surrendured to you.

This has happened to Karavox in my current game. If I mouse over him he's listed as "immobilized" for 1 turn. But the immobilization doesn't expire, the next turn the mouse-over says the same thing.