You can obtain the Leftovers item in Pokémon Black 2 as of three ways:
- Find it in Castelia Sewers near the Doctor.
- Trade it from another Generation 5 Game.
- Or by levelling up a Pokémon with the Pick Up Ability to between level 81- 100. You will have a 1% chance of picking it up.
If you need more help trying to find Leftovers in Castelia Sewers, you can watch a video walk through here.
For a list of Pokémon with the Pick Up Ability click here.
Hope I helped :)