Misfit is a handled fiddle box with a lid and no matching bottom. A fiddle box has a lid with a matching bottom.
Marlin had a Misfit at Nashville that was Snakewood/Butternut(I think) that had a Snakewood sleeved bottom. This was the only Misfit I've seen this way, and it wasn't a full "base" it just fit flush with the Butternut and profile of the call body. I wish I would've taken pictures of it, it was an awesome call.