What happens to a warder when his Aes Sedai is stilled?

[Bentrudagi]

I just re-read the battle of Dumai's Wells and it got me thinking what happens to the warder of a stilled sister? The two events that come to mind with stilling happen there and when Siuan  is deposed. For Siuan and Leanne their warders were killed in the battle, and I didn't see any mention of what happened the the warders of the stilled sisters at Dumai's.

So is the warder bond broken? Does the sudden break cause as much emotional harm to the warder as it does the sister?

Just curious if there is a scene I can't think of that answers this, or if RJ or BS ever answered the question.