The last point of damage will continue to float between the guardians until the chain is broken
When one of the guardians takes damage, then half of that damage remains on the guardian, and the other half gets passed onto the next guardian. That guardian will then take half and pass half on. So forth and so on, until there is only a single point of damage left. Because the damage being passed on is rounded up, that half of 1 becomes 1, and that one point is continuously passed between the guardians.
The "floating" point (pardon the pun) has no effect.
The creature being protected by a guardian never feels the effects of the damage that is redirected to the guardian. If you are at 8 hp and are dealt 10 damage you do not start making saving throws before the guardian takes 5 of that damage away from you. Since each of the guardians is being protected in the same manner, none of them ever feel the effects of the point.
When the loop is broken, the point will immediately be permanently applied to whomever is now last on the chain.
Each instance of damage will create it's own looping point.
Multiple looping points of damage would not be in sync with each other, and therefore they would not be able to split and leave half behind. Even if you wanted to argue that that is what should happen, there's no way to determine which guardian they should end up on.
In theory you could use this to "store up" an arbitrary amount of floating damage, which would all be immediately inflicted on the last guardian of the chain once the chain is broken. But unless you can figure out how to make that last link something you want to kill, I see no practical way to abuse this loophole.