Tig's explanation gives the logical reason for the behaviour...but of course things aren't always logical. The sides of a road wouldn't bend like that, for instance. I thought some time ago about requesting a new feature for the Offset Tool, activated by holding Ctrl down, but thinking more deeply, it's one of those situations in which the software can't read your mind; it has no idea which lines you want to remain parallel and which to 'doctor'.
Mostly, I do what Tig has done and simply delete the weird bits (much easier with the last couple of versions that allow edges to self-intersect) If you really do want to maintain some kind of predictable curvature on the offset, having exceeded the centre of curvature of the outside corners, then use the maths demonstrated in the diagram. This effectively shifts the centre to the middle of the square...so you can run a number of concentric offsets with uniformly smaller corner curves.
The easiest solution is, of course, to work from the inside and offset outwards...then you don't get any of these problems and the corner curves will remain mathematically parallel...but probably more rounded than you want by the time you reach the exterior.
[image: h7z3_fillet_thumb.jpg]
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