In fighting the Shadows, sometimes your party members will be struck down with critical or weakness strikes, putting them in a Downed status much like your enemies can be thrown into. If this happens, there is a chance the Shadow will take your party member hostage and try to negotiate with you some terms of release.
If you are playing online with the Thieves Guild network active, you can ask for aid from them to recover the hostage without losing an item. Otherwise, if you agree to the terms, you will be able to get your party member back. Failure to meet demands will cost the party member their life and they will faint.