A: Which brothel did you say she worked out of?
B: I didn't. She works down there, at the back of a hat shop.
From TV show Desperate Romantics
The expression is to work out of a shop/cafe/room or whatever.
It implies that the location is not very salutary. You wouldn't say that the president of a company works out of a large office.
The sentence suggests that the woman concerned is a prostitute. You could say that she works in a brothel. To say that she works out of implies that she uses it as a base.
The of is merely at the end of the sentence. You could rephrase it as: Out of which brothel did you say she worked?