Accordion lampshades are a stiff pleated material. The pleated lampshade cover is on a plastic liner. Most often the spider wire (top wire) and bottom ring are attached to a plastic liner with paper tape or grosgrain.
Pleated Accordion Lampshade
Over time, the paper tape or grosgrain deteriorates and the wire lets loose off the shade. This particular old shade was one of a set of lamps and the top paper tape gave loose from this lampshade.
I cleaned and waxed the spider wire before attaching it back to the shade with grosgrain. The liner of the shade was old and brittle, so patience was a major factor in reapplying the wire to the original plastic shade liner.
Pleated Accordion Lampshade Wire Repair
Pleated Accordion Lampshade
This old shade cover has a wood grain fleck in the pleated material. A very pretty warm light