...not sure what you mean here. If all the close-up detail is done via textures you wouldn't need (and wouldn't be able to use) detail boxes in the first place; those are for geometry.
You could theoretically have a duplicate building in the detail box, overlapping the normal one, with some higher-res textures applied to it, but this could be done in one of two ways:
The buildings in the detail box use a single (or a few) very high-res textures, replacing a single (or a few) lower-res textures on more distant buildings, in which case the lower-res textures are redundant as they could just be mipmaps of the larger ones, or
The buildings in the detail box use a bunch of different hi-res textures allowing for greater variety, in which case you run into engine issues for using too many textures (and see popping as the textures change from the distant to the various hi-res versions).