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Placed cards like WWW follow the character they are placed on wherever they go (hand, deck, discard). I believe they are discarded when a character is captured, but hopefully someone can confirm or deny that with more certainty
Placed cards are not discarded, that's weapons.
The burden of proof is on saying they are discarded. No rule indicates that they would be discarded.
...I'm not trying to argue I'm not looking for the "burden of proof" just where the rules are to describe what happens to these cards. Or rulings in the past. Having a hard time finding them, and was looking for some help is all.
There isn't a bottom-up rule. Placed cards stay on and follow their hosts. There is no rule that makes an exception for capture.