Short stacks have little to lose and are eager to double up. They don’t have the luxury of waiting for premium hands like the big stacks, so they’re forced to gambling more often with marginal hands. You can use this to your advantage by raising somewhat marginal hands preflop, but only if you’d feel comfortable calling an all in.
An example of when having a short stack around can be beneficial is during the bubble of a tournament and sit&go. Players with comfortable stack sizes will often be reluctant to take any risks until they make it into the money. During this situation you can constantly needle these players and steal the blinds and small pots.