The death ward spell states:
[...] If the spell is still in effect when the target is subjected to an effect that would kill it instantaneously without dealing damage, that effect is instead negated against the target, and the spell ends.
One example of such an effect would be failing a third death saving throw. Ordinarily you would die immediately after failing your third death saving throw but this is not the case for the Zealot Barbarian currently Raging Beyond Death:
You still must make death saving throws, and you suffer the normal effects of taking damage while at 0 hit points. However, if you would die due to failing death saving throws, you don't die until your rage ends, and you die then only if you still have 0 hit points
So what happens if the Barbarian has three failed death saves and then their Rage ends?
What instantaneously killing effect is the Barbarian being subjected to?
What exactly is negated by death ward?
Is the third death saving throw removed?
I believe my question is different from "What happens when you cast Death Ward on a raging level 14 Zealot Barbarian who is at 0 HP?" because that one asks about taking damage while at 0 hit points with death ward cast whereas mine is asking about death caused by three failed death saves.