This discussion may contain spoilers!
Faith's donkeyskin coat is quite an enigma. It's possibly red herring unrelated to the murders of Faith and Lily, but even so, I can't figure out why it was stuck inside Toad's char.
That coat itself might be of some value to Fables. It is a magical coat that, in the case of Faith, glamoured her long ago to make her look like something less than the most beautiful girl in her father's kingdom. It was made from her father's magic donkey that would poop gold when prompted. Presumably that power ended when the donkey was skinned for Faith's disguise. It may be valuable in the right hands, but it's not obvious how that would be.
Now, ow did it get inside Toad's building? She didn't bring it with her when she went to see the Woodsman; it's not something she'd wear on a "date," and she doesn't take it with her when she leaves. Yet the next day Toad has it hidden in his chimney, and implies that he confiscated it from a previous tenant. But Faith had been living with Lawrence in that building, not in Toad's building. So where/how did Toad get his webbed mitts on it? (Also worth noting: Toad lies a lot.) Still, it's aggravating that Bigby didn't question Toad further about it or Faith.
Also, Toad says that the Tweedle who assaulted him and Toad Jr. wasn't after the Coat. If not the coat, then what else could either Faith or the Woodsman have of any value to them? (The Woodman's magic axe?)
Finally, it looks like Faith left a short farewell note on the coat, for Lawrence. Why would she leave a farewell note on her most prized possession that she then "left" at a rundown apartment building that she, maybe, never even lived at? Did she mean for the letter and the coat to go back to Lawrence?