Intermittently - and more likely on servers - the world border can become "mis-aligned" in the Nether causing unavoidable suffocation, as well as prevent the player from breaking or placing blocks.

This isn't a small misalignment - I believe the Nether is temporarily setting the world border centre to entirely new co-ordinates, even though it is physically shown to be in the right place and can contain players as normal (see 'the cause' below for further details).

Closing and re-opening the world (single player) or restarting the server (multiplayer) resolves the issues for players. However this isn't currently possible on Realms, and isn't a great experience during gameplay.

Suffocation example
If a world is loaded with the world border set at a low number (1), and then the world border size is increased (to 10 for example), when players enter the Nether, they will be suffocated immediately. This happens even if the world border damage amount is set to 0, and the world border damage buffer is set to a large number (9999999999).

As an attempt to work around this bug, the world border could be set to a larger number (9999999) and then reduced when the player first enters the world. This solves the instant suffocation, but then causes the following issue:

Unbreakable/unplaceable blocks example
If a world is loaded with the Nether pre-generated and a small world border size is then applied (1 for example), and then increased (10 for example), players won't suffocate, but will be unable to break or place blocks in the Nether. This isn't like being outside the world border - blocks begin to break/show when you place them, but instantly reset/disappear. Any blocks attempted to be placed are removed from player inventory in game modes 0 and 2.

Note: Through my testing, this only seems to be happening on worlds where the Nether has already been entered/generated. If you start a new world and enter the Nether, you won't be able to reproduce this issue. But if you then take that existing world with generated Nether, host it on any server, and perform those steps again, it'll happen.

The cause
It seems the Nether is not great at tracking how large world border is currently set - or more likely - where the exact centre of the world border is set. While the unbreakable blocks issue is happening, setting the world border's size to a large value (9999) allows you to place and break blocks again. Set it back down (10) and the issue returns.

Here's the biggest clue to the bug I've found so far - if you change the world border size to 50 while in the Nether, you may find an area within the visible world border where you can break and place blocks. My guess is that the world border thinks it is centred nearby, even though there is a visible world border that keeps the player contained. In fact, if you fly around with the size set to around 50, and then enter this "second" (invisible) world border, it will actually prevent you from leaving it while in game modes 0, 1, or 2. You'll hit an invisible wall, even though you're already inside the visible world border.

After some testing, if you use commands to re-centre the world border again to its overworld co-ordinates, it seems to correct this issue without needing to restart the server or close and reopen the world. Even though there's no visible change to the world border in the Nether, it seems to correct the second invisible border. So for the moment, there is a work-around at least.

Confirmed in 1.9, testing in newly generated worlds.