Taking Damage while Dying or Stable
While you are dying, if you have any Stamina Points, any damage you take still reduces those first. The first time each round you take Hit Point damage (whether from an attack or from continuous damage, such as from a bleed effect), you lose 1 Resolve Point. At any point after that in the round, if a single source (such as one attack) deals Hit Point damage greater than half your maximum Hit Points but less than your maximum Hit Points, you lose 1 additional RP. As mentioned earlier, if you would lose Resolve Points but have no Resolve Points remaining, you die instantly. If you take damage equal to or greater than your maximum Hit Points from a single attack, you also die instantly.
If you take damage while unconscious but stable, you are once again dying and no longer stable.
Source
Core Rulebook pg. 251