bottom part of some shoes
a half sole inserted between the insole or welt and the outsole of a shoe to give additional height
— Merriam-Webster
an extra sole on a shoe located between the insole and the outsole
— Collins
A half sole running from toe to shank, between the regular outsole and the welt or insole. The term “slip sole” is also applied to a thin insole, which is slipped into the shoe either to add warmth or to adjust it in fitting it to the customer’s foot.
— The Shoe and Leather Lexicon, Fourth Edition, 1918