Blender Version
Broken: 2.79b

Short description of error
When bevelling something with texture coordinates, it usually looks really weird.

Exact steps for others to reproduce the error
See attached.

Top left: unbevelled
Top right: 2-segment bevel modifier
Bottom left: 4-segment bevel modifier
Bottom right: What it should have looked like — 4-segment bevel modifier applied and then manually fixed up

Sometimes coordinates can be fixed by scaling them by a factor of 3 with the cursor set to the coordinates of another face.

Screenshot:

Test case: