Related – How does one dispatch a helpless opponent?
Here's the unconscious condition description:
Unconscious
An unconscious creature is Incapacitated, can't move or speak, and is unaware of its surroundings
The creature drops whatever it's holding and falls Prone.
The creature automatically fails Strength and Dexterity saving throws.
Attack rolls against the creature have advantage.
Any attack that hits the creature is a critical hit if the attacker is within 5 feet of the creature.
So attacks against the creature have advantage, and any attack that hits is a critical – but you still can miss because of the creature's AC. Armor Class includes dexterity bonus. The description doesn't say the creature's AC changes somehow.
Does it mean the creature still benefits from its dexterity, both in terms of mechanics and in-game world?
An example situation
A low-level party of Barbarian and Bard fights a sneaky thief, who has AC of 15 due to his +4 dexterity bonus. The Barbarian attacks, so does the Bard, but their results are 12 and 13. DM described that the thief was twisty enough to dodge both attacks.
Next round, the Bard puts the thief to sleep (hence, unconscious) with the Sleep spell. The barbarian makes a melee attack with advantage, but his best result is 14. It is still a miss, isn't it? As a DM, how can I plausibly describe such an outcome?
Best Answer
The gist: your Armor Class remains the same despite being unconscious. You can justify a miss by saying the unconscious target was not hurt by the attacker's careless attack.
Yes, your AC is still kept the same
Your thief's AC is 15, before and after succumbing to the sleep spell. That is simply how AC is calculated (Base AC of Armor + Dex mod), as written in PHB 144.
Followed by the AC specified in PHB 145 on how to calculate Armor Class from Padded or Leather armor: \$11 + \text{Dex modifier}\$
How is this narratively justified?
Armor Class is not how hard you are to hit, but how hard you are to wound.
The difference is usually immaterial, but in this case, it is important. The Barbarian could still have hit the Thief, they just failed to hurt them.
We can also take guidance from how Armor Class is calculated for objects:
Objects cannot dodge, much like a sleeping creature, so you instead use AC to represent how hard it is to damage the object. Interestingly, the following ACs are used for the brittle materials:
\begin{array}{|c|c|} \hline \textbf{Substance} & \textbf{AC} \\ \hline \text{Cloth, paper, rope} & 11\\ \hline \text{Crystal, glass, ice} & 13\\ \hline \text{Wood, bone} & 15\\ \hline \end{array}
Your unconscious Thief, as it turns out, has the same AC as bone. This means, even after being hit by something (because it can't dodge), bone is still difficult to damage. It is probably resilient enough that you cannot crack or snap it in one blow.
In other words: you can let your Barbarian's swing hit the Thief, but you can justify by saying, despite the impact, did not actually hurt the target. They could bruise, or get a cut, or a small puncture wound, but the nature of the blow is such that the target was not meaningfully harmed.
Also narrate the failure of the Barbarian
Despite having Advantage, your Barbarian's best roll was still a 14. That is a failure on their end, not just a product of the resilience of your unconscious Thief. Focus on that as well.
You can say that the Barbarian thought they were aiming for the head, but they lost their footing slightly during the swing, or aimed too quickly or too excitedly, or the hilt on their weapon slacked just a bit. You can also add an external factor to the blow, and use that external factor to explain why they failed to deal damage.