Interior trim nailing material

[jhowes]

When I removed the interior rear side panels ( the ones that fit in the curve in the rear corners) I found that there is a channel that holds some sort of material up at the top of these curved panels which I assume is for holding the nails that hold the side panels. Does anyone know what that material is and what to do to replace the deteriorated core of these channels? My car is a 31 tudor. Jack (thanks in advance)