The recipient of bardic inspiration must be able to hear the bard.
...choose one creature other than yourself within 60 feet of you who can hear you.
An unconscious creature is "unaware of its surroundings."
An unconscious creature is incapacitated, can't move or speak, and is unaware of its surroundings
Can creatures can still be affected subconsciously by things they hear while they are unconscious, despite being unaware of their surroundings?
The rule for unconscious says:
can't move or speak, and is unaware of its surroundings
It is interesting to note that it does NOT say:
can't move, speak, or hear.
There is no definition of "surroundings" in the game but a plain English understanding would be something along the lines of "all the stuff (physical structures, terrain, creatures, etc) around the unconscious creature.
That "stuff" often produces noise and a character, hearing that noise, would be aware of (some of) her surroundings by definition. In other words, a character can't both be unaware of her surroundings but still hear them. So, given this strict reading of the rules, the Bard can't convey inspiration.
However, the fact that hearing is not literally excluded seems very telling. We know that people can perceive sound when asleep and that even coma patients may still be able to perceive some external stimuli.
So the fact that the rule for unconsciousness is worded a little vaguely suggests that a DM allowing the Bard to convey inspiration would not be out of line given a reading that assumes an intent to simulate actual phenomenon instead of just a strict interpretation of rules wording.
The description of the unconscious condition says:
can't move or speak, and is unaware of its surroundings
If there were some ambiguity around awareness with being unconscious, these rules quell that ambiguity by stipulating that a creature that is unconscious is also unaware.
It is likely the word “unaware” is used because many creatures in D&D have unusual senses; creating an exhaustive list of senses that do not work is untenable.
Usage of the word “unaware” is not vague, but carefully chosen to encompass a wide interpretation.
Further, reading the description of the Bardic Inspiration feature:
You can inspire others through stirring words or music.
This invokes a sense that the feature rouses strong emotion, excitement or motivation in the target.
Since an unconscious creature is unaware of the words or music, they cannot be stirred or inspired by them. A bard's performance does not benefit a creature unaware of it.
