There are some styles where the accompanying motif is not in the game yet. Those sets will not yield style stones until that motif is added to the game.
Sometimes they will drop the style mats before the motif is actually dropping, but has been added to the data files (it will show in the achievements as a motif to learn).
This has been fairly standard, especially for DLC dungeon sets/styles, where the motif doesn't come out until 4-6 month later for "replayability"
I may be misunderstanding you, pardon in that case, but... there are no traits for sets? Do you perhaps mean special style material, special material to make a craftable set in that particular style?