Nevermind, found the music, but still don't know about the sword. It is even possible to repair or is it just an easter egg from a different game?
you will eventually get metal (iron) that you can give her when you use her skill to "reforge" the weapon if it is in your inventory and not equipped.
I have iron, I have the Rusty Short Sword, I can 'reforge' weapons, but I still can't do anything with the Rusty Sword. It just asks me to give her Steel or Damascus Iron and I checked the Damascus Iron and no Rusty Short Sword.
