This discussion may contain spoilers!
After reading a few threads today, I've been inspired to come up with another theory.
Maybe Faith wasn't just a hooker, maybe she was also a thief and woody just so happened to be her target. Since most of the fables know each other and since Woody does like to hang in rough part of town. Faith could have known that Woody didn't have much in money, but did have certain magical/blessed item in his possession ( his axe).
The person who she is working for has some magical abilities and potent enough magic to stop the Magic Mirror from finding a dead girl's body.
I think that Lawerence and Faith got in with the wrong crowd or owed someone big time. Faith became a working girl to keep whoever they owed money to from killing Lawerence. Her pimp knowing she could never pay off the loan-shark as a regular working girl purposed that she steal magical items from the fables she interacts with ( she could only do this while they were sleeping and such maybe she could slip them something) . This would speed up the process of paying off the debt and she would be free.
If that's not the case then it could be just in this particular instance that Faith's employer wanted what they thought Woody had.
The piece of evidence that backs up my theory are the Tweedles. Why is Dumb going through Woody's apartment? He obviously wasn't after Faith belongings, when Toad offered Dumb her coat he didn't want it. When you catch Dee for the first time he says that He and Bigby are both after Woody and when at the Lawerence residence, Dee is not interested in the Prince, but the books on the shelf possibly indicating that whatever it is, it's small enough to hide in a book or it's a part of the book ( possibly a spell or map).