The problem is that you and i are coming at this at two different angles. We dont see this world the same way. Since most slaves are criminals there isnt as much protest as their would be otherwise. This way people arent paying taxes for a prison. Criminals pay their debt off by servingothers. The collar depends on the crime that the person is accused of committing. Lesser crimes, like theft would get a collar that could be removed once the person served their time. All crimes are magically bonded to person. It can only be taken off by the head prison mage. So removing would be impossible. Hiding it would be had since the point of the collar is to identify her as a slave. Liz collarwould be thick and pretty obvious since she's was convicted of murder. When I play a slave I have a legitimate reason for them to be bound in such a way and a way for them to be free once the quest is done but not before than. 

Even work the limitations of her being a slave the task of finding this bladed beauty is impossible. She is being sent into a building full of people. This building can have anywhere from 5 to 100 people in it. All of them the possible beauty. There is no way for Liz to identify who she is looking for and asking each person if they are the beauty isn't going to accomplish anything. Without a way of identifying the bladed beauty this task is pointless.