On servers where there is a world border present, you can quarry beyond it with the builder. Also, since you can modify the offset as much as you want on the quarry card, you can infinity mine beyond the border.

No to infinity. There is a limit in the offset at about 512 by default I think

As to world border, not sure what to do about that. Is there some way I can avoid going beyond the world border? I have no clue how that is implemented

Oh, I didn't realize there was a max to the offset. I thought the restriction was only on the size. Maybe this isn't as big of a deal as I thought. I also just assumed that forge had some query that would give the world border. I should have probably researched a bit more before posting. sorry.

Well it is possible that there is something but I'm not aware of it. If you or anyone else finds info on this subject then it would be nice to inform me of that in this ticket. Perhaps I can do something about it

You can get the world border from World#getWorldBorder() and if I remember correctly it has methods to get the center point and the diameter. Then you can clamp the positions to within that area as needed.

Also I believe there was something weird going on with the world border at least in the Nether. I think it returned the default 60M blocks wide diameter on the server (unless I derped up something), but on the client it is still visually where the overworld border is (which is also weird, why didn't they make it a 1/8 size from the overworld, or better yet, per-dimension... not to mention allowing different dimensions on the x and z axis etc... :/), or something like that. It has been a while since I touched that code.