~~~ if it rested on top.

Your examples are true inlays and, what you might be seeing on the edge is simply oozing of compressed material if they were so constructed in that manner.

Some of the older Italian metal-center filigrees (most known in private collections) are stud-mounted overlays where only those anchors are keeping the overlay secure.

Some die-cut metal inlays were textured on one side (and both sides) while most of the disloged and never used inlays were smooths on both surfaces. I sent Jim B. examples in 1993 of those, but he had no idea who made them. Neither did BG at the time.

Btw, I saw several Tahoe Village $5 metal die-cut inlay chips which were reset; crudely... and buffed.