The bug
Unlike other things in the world such as blocks and entities, the world border behaves quite strangely with respect to fog and camera distance.
Objects in the world will generally render with full intensity, until at the edge of the render distance, after which they will fade to the fog colour. However, for some reason, the world border ignores fog, and will continue to render until being sharply cut off at the end of render distance.
In addition, while inside of the world border, the texture will fade when far from it, which makes the position of the world border non-obvious when far from it, as it can basically appear out of nowhere when you get close even though it was invisible yet within visually rendered chunks.
When outside of the world border, no fading happens at all (MC-225823), and it continues to render in very unloaded chunks.
How to fix
Make the world border fade away correctly with fog, rather than the weird broken system it currently uses.
Can confirm.