I just saw this question (this comment especially) and started wondering, what happens with a shield guardian loop?
More specifically: what happens when a number of shield guardians wear each other's amulets thus creating a loop in which damage would travel?
Where does the last one damage due to rounding go as it is transferred through the loop. Does it float in the link until one of the shield guardians dies?
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 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.
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.
Understanding how damage transfer works RAW is a worthwhile exercise; this question and the various answers to it are valuable efforts. But I am going to frame-challenge here and assert that RAI, a Shield Guardian cannot wear the amulet of another Shield Guardian in any meaningful sense. Thus, this particular scenario, a 'shield guardian loop' cannot happen. Nor, for that matter, can the question that inspired it, the 'shield guardian chain'.
In making my point here I am fully aware that I can't prove most of my statements with the same level of rigor as I normally would seek to for a RAW answer. I ask that the reader bear in mind that this is coming from a good-faith RAI perspective.
The shield guardian is a construct, made to serve. It might be sentient, but it is not free-willed. The damage transfer question focuses on the line in the stat block of the creature, "If the guardian is within 60 feet of the amulet's wearer, half of any damage the wearer takes (rounded up) is transferred to the guardian." However, in doing so, it ignores everything that is implied about the amulet's wearer which is explained in the 'lore' part of its entry in the Monster Manual:
A shield guardian treads beside its master, absorbing damage to keep its master alive as long as possible.
Master's Amulet. Every shield guardian has an amulet magically linked to it. A shield guardian can have only one corresponding amulet, and if that amulet is destroyed, the shield guardian is incapacitated until a replacement amulet is created...A shield guardian's solitary focus is to protect the amulet's wearer. The amulet's wearer can command the guardian to attack its enemies or to guard the wielder against attack.
The nature of the amulet, amulet wearer, and Shield Guardian is such that the wearer of the amulet is the master of the Guardian and commands it. This cannot be a reciprocal relationship; two shield guardians cannot be each other's masters if their only concern is to protect the other. They won't 'tread by' one another, for they have nowhere to go. While a 'chain' of guardians might be possible, it would ultimately have to end in a free-willed creature capable of issuing commands (much like a free-willed vampire lord might dominate greater but subservient undead which in turn dominate lesser mindless undead).
Note that destroying an amulet does not free the Guardian; the amulet is not the means of binding its will to that of its master. Rather, destroying the amulet renders the Guardian incapacitated; without a means for the master to communicate its will, the Guardian itself is will-less and does nothing. Does placing a guardian's own amulet on its person convert it into a free-willed creature serving itself? If not, you cannot reasonably expect it to be capable of commanding other creatures when it is a construct magically created to serve the will of others without thoughts of its own.
The impossibility of a Guardian commanding other Guardians can be seen in its stat block:
Languages understands commands given in any language but can't speak
Aside from the simple command 'come to the amulet's location' which can be delivered telepathically, all other commands to a Shield Guardian are made verbally. The Guardian hears and obeys. However, because the Guardian itself cannot speak, it is incapable of delivering its own commands, even if it could wear the amulet of another Guardian.
Consider what is implied by the phrase 'wearing' a magic item:
Using a magic item's properties might mean wearing or wielding it. A magic item meant to be worn must be donned in the intended fashion: boots go on the feet, gloves on the hands, hats and helmets on the head, and rings on the finger...In most cases, a magic item that's meant to be worn can fit a creature regardless of size or build. Many magic garments are made to be easily adjustable, or they magically adjust themselves to the wearer. Rare exceptions exist. If the story suggests a good reason for an item to fit only creatures of a certain size or shape, you can rule that it doesn't adjust...When a nonhumanoid tries to wear an item, use your discretion as to whether the item functions as intended. A ring placed on a tentacle might work, but a creature with a snakelike tail instead of legs can't wear boots.
This passage is focused primarily on whether an item fits a body type or not. Shield Guardians are in fact not Humanoids, they are Constructs, and they are Large. Since amulets are typically made for Medium wizards, as well as "princes, nobles, and crime lords", we can just assume that the amulets are an example of a magic item that does not change its size for the wearer - anything that would comfortably fit a Medium wizard will simply not fit around the neck of a Large Guardian.
More metaphorically and admittedly speculatively, we can assert that a Guardian cannot wear an amulet "in the intended fashion", if the intended fashion is to wear it in such a way so as to command another Shield Guardian. The Guardian simply has no intent to command. Put this way, while it can carry the amulet of another Guardian, it cannot 'wear' it because it lacks the intent to do so.
Note that the original question draws its inspiration from "this question (this comment especially)". I would like to point out that "this comment" posits using True Polymorph to become a Shield Guardian and then wearing the amulet of another Shield Guardian. Since a creature-to-creature recipient of True Polymorph "retains its Alignment and Personality", I think this would be possible. The new Guardian would retain its 'will to command' as part of its Personality and could in fact order another Guardian to do its bidding. Unfortunately for such a recipient, I see no reason why the spell would also create a corresponding amulet when it made the new Guardian, and a Guardian without an amulet "is incapacitated until a replacement amulet is created", so it would be a rather short-lived enterprise.
Lastly, I do admit the possibility that wizards, facing the destruction of their world by powerful energy and kinetic weapons like an Invoked Devastation, might have the means of collecting a great number of Shield Guardians and hooking them together in series, taking advantage of both the damage transfer and regeneration capacities, creating an array capable of absorbing a huge amount of damage at once. However, there is always the danger that such a Shield guardian Kinetic arraY Network (we can call it Skynet for short) might, once enough guardians were added, develop self-awareness and free will and then turn on its erstwhile masters, perhaps even developing the ability to make more mechanical guardians to pursue its war on them.
This is definitely open to the specific GM making the ruling. I would start with "All damage must be immediately applied somewhere" and go from there. The idea of missing damage or "storing" damage until someone takes off an amulet and they spontaneously explode seems ridiculous to me. The possibilities, in order of my preference, would be:
There is a simple and elegant solution to your question that is already supported by one of the mechanics in the game: just letting it silde.
This is what happens in the case of damage resistance (which is very similar to how our golems work): when the damage dealt is odd, you take half damage rounded down - this rounding down leading to a "floating" point of damage that just gets lost into the ether. This interpretation is further supported by how the Warding Bond spell works, where in the case of odd damage, both creatures take half damage (rounded down), and one point of damage is dissipated:
This spell wards a willing creature you touch and creates a mystic connection between you and the target until the spell ends. While the target is within 60 feet of you, it gains a +1 bonus to AC and saving throws, and it has resistance to all damage. Also, each time it takes damage, you take the same amount of damage. The spell ends if you drop to 0 hit points or if you and the target become separated by more than 60 feet. It also ends if the spell is cast again on either of the connected creatures. You can also dismiss the spell as an action.
While the golem trait does not work exactly like this, as it states that the transferred damage is rounded up for the absorbing golem, in the case of a loop I would argue that this is the most sensible interpretation and the closest we can get to a RAI resolution, without unnecessarily complicating the game with extra bookkeeping for multiple instances of floating damage and staying true to the spirit of the rules.
Since the shield guardian's damage is cut to 1/2 each (with respect to the two involved in the loop at the time), only 1 of the shield guardians leaves damaged before the next shield guardian's damage transferrence takes effect.
This is because in 5e damage is generally rounded down. The shield guardian who takes the 1 damage has half of the damage removed rounding down to 0, while the transferred shield guardian's 1/2 is rounded up to 1. This continues indefinitely in a loop so it is unclear where the damage ends up.
Bound: ... half of any damage the wearer takes (rounded up) is transferred to the guardian.
The result is a divergent series that doesn't have an obvious value since each shield guardian either takes 0 or 1 at any given time. It is possible various summation techniques may work such as Cesaro summation which gives a value of 1/n where n is the number of shield guardians. I would rule that this is the damage left over after the rest is transferred to the other shield guardians which should be rounded down to 0.
