The drop in midsole is usually found on shoes which require alot
of grip: such as a skateboard shoe or a racket ball shoe. The drop
in midsole does this by putting the foot lower to the ground, but
also providing enough cushioning to support the foot. The history
of the drop in midsole system is somewhat murky: DVS SHOE CO., INC.
applied for trademark status of the technology, but, at present,
it would appear this application has been abandoned. There are plenty
of well known shoe brands who use a drop in midsole in their footwear
- such as DC's The Park Boot, and Nike's Leshot lt bone.