It looks like it may be the remains of a Jostam Sponge Rubber pad or one of its predecesors. They came in single layer, double layer and triple layer styles. In 1918 catalogues its the S & R Recoil pad. By 1925 its the Huntley Shock Absorber. By 1929 they are part of the Jostam line of recoil pads and remained in their line into the early 1950s.