The section on "Stabilizing a Creature" states:
You can use your action to administer first aid to an unconscious creature and attempt to stabilize it, which requires a successful DC 10 Wisdom (Medicine) check.
A stable creature doesn’t make death saving throws, even though it has 0 hit points, but it does remain unconscious.
This method of stabilizing seems to require that the creature be unconscious. Perhaps this is not the case, but is there ever a time where it matters - a time where a creature has 0 Hit Points, is conscious, yet unstable?
I would like answers to use "official" content; no Unearthed Arcana, Homebrew, or Twitter/Stream material should be considered.
I have only found one time where this matters, which is the Zealot barbarian using the Rage Beyond Death feature. In this case, you cannot stabilize this barbarian using a Medicine check.