When the game is paused from ESC, the World Border still moves using /worldborder add <blocks> <seconds>.
It is not just the animation, if you are outside the World Border after you've unpaused the game from this bug, you'll get damaged and die.
Also, as strangely as it sounds, the death message is "<player> suffocated in a wall".
Linked issues
Comments 4
This is working as intended; the world-border is the only real-time clock available in a running game.
Although from the wiki, "The border will still grow or shrink and the animation will display even if the game is paused", I guess I should admit that I didn't see that. If other things can be paused in singleplayer, why is the World Border can't be paused?
However, after I just noticed that according to a dev comment from MC-53491, "The world border is a server-side mechanic to restrict the area accessible to players. Servers are not supposed to be paused. Time is constantly passing on servers, therefore the world border is constantly updating. We might revisit this after 1.9, but for this release it's too risky to change (and potentially break) this mechanic."
Why in the world is it placed as "resolved", should just leave it be as "open" or "in-progress", this will just prompt some people to duplicate the issue, or like I did. After all the last report was somewhere at 1.8, this is minecraft snapshot 16w05b, or 1.9 in the future update. It should be fixed sooner.
Duplicate of MC-78516.