Generally speaking for the Con quests I have been given in the past. They were all items related to my role, and they weren't just one specific item, but it was left somewhat open to your interpretation of the item in general and obviously the more religiony/better suited the item I would imagine the better reward you may receive.

Also, ID will not say if it is the correct item, some items can be located, there is no way to detect the item and there is no real displacing.

Of course this would depend on the quest your talking about

Lets say Lich/Mummy quests...some of these items are locatable. IMM given quests, again they could be.