In what ways can a creature have zero Hit Points, be conscious, and be unstable?

Question

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.

Answer 1

The Samurai feature Strength Before Death gives a character a single turn where they are conscious, at 0 Hit Points, and unstable.

The Samurai archetype of Fighter, found in Xanathar's Guide to Everything (p. 31), has the 18th-level feature Strength Before Death:

If you take damage that reduces you to 0 hit points, you can use your reaction to delay falling unconscious, and you can immediately take an extra turn. While you have 0 hit points during that extra turn, taking damage causes death saving throw failures as normal, and three death saving throw failures can still kill you. When the extra turn ends, you fall unconscious if you still have 0 hit points.

Once you use this feature, you can’t use it again until you finish a long rest.

The Fighter is conscious but at 0 Hit Points and unstable, so they wouldn't be able to use their action on their extra turn to make a Medicine check and stabilize themself before falling unconscious again.