Before heading into the crater in Carbon, talk to Ruby and she will give the Initiate this side quest. It seems her cat, Mr. Pussy, has managed to get lost in the crater. The cat can be found, dead, in a house in the first set of buildings encountered in the crater. It's in a room in a building to the right, when coming from the crater entrance.
Once finished in the crater, return to Carbon, complete Town Under Attack and then find Ruby in the warehouse, where she hid from the raiders. The Initiate can then return her dead cat and she will tell the Initiate she has lost yet another thing, her necklace, starting another side quest.