Early Brake type - pulling on one side

The only thing I can think of, is that I seem to recall seeing shoes that may have used different material for each shoe in a pair. But still...

 

The orientation for the shoes is dependant on the anchor system. Older brakes had both shoes bolted into the bottom of the backing plate so the larger shoe went to the front. Later, they went to the single anchor or floating anchor or also known as self actuating. The smaller shoe went to the front in these systems.