Cloth simulation problem

I have been attempting to do a cloth simulation which has patches of a separate type of material. Say like  a long strip of embossed leather stitched onto some sort of fabric. Is it possible for the more rigid material to slightly deform to the shape of the cloth while still mostly maintaining its shape?


Originally I made a plane and sculpted details onto it around the edges, but these details were lost after the simulation (which makes sense in retrospect).

Edit: attached an image to illustrate what I am trying to do. The design on top of the cloth would bend with the cloth but not as freely. After bending it would still be bumpy.