Sectors, to my understanding, don't necessarily assign themselves to linedefs and points. When sectors are unclosed, they still occupy the same space. However, the linedef that should've been in existance to provide the textures needed probably was deleted. Therefore, the missing texture can't show up, because your linedef is gone.
In other words, never delete a linedef unless you are sure of what you are doing.
A rather complicated solution is to draw a linedef in where one was and check (playtest) to see if it worked. If the lineddef still doesn't work, make the font and back sidedefs the sectors on the respective side. (Sector : ___ ) And if you are still having a problem, create a sector around the problem linedef (or lack there of) and delete it. The selected area should be hollow. Now, using the vertices mode, carefully reconstruct what was supposed to be there, carefully creating and dragging veritices when necessary. And if you still can't fix it, I'd be happy to take a crack at it.