The demilich (MM, p. 48) has the following action available to it:
Howl (Recharge 5-6). The demilich emits a bloodcurdling howl. Each creature within 30 feet of the demilich that can hear the howl must succeed on a DC 15 Constitution saving throw or drop to 0 hit points. On a successful save, the creature is frightened until the end of its next turn.
A party of adventurers faces a demilich. One of them is a paladin with the 10th-level feature Aura of Courage:
Starting at 10th level, you and friendly creatures within 10 feet of you can’t be frightened while you are conscious.
The demilich gets close to the party (who are all within 10 feet of each other), and uses its Howl action. The paladin fails the save, while their friends succeed. Are their friends frightened?
- The Paladin will be reduced to 0 HP, and thus unconscious. When that happens, their Aura of Courage will stop working.
- We know from Does a Paladin's Aura of Courage prevent or suspend frightened effects? that if the Aura of Courage is up when the frightened effect tries to apply itself, the Aura going down after that will not mean the effect resumes; it was initially prevented entirely, and so is not merely suspended.
So the only question that remains is:
Will the Paladin still be conscious at the point the Howl attempts to apply the frightened condition to the party? Or will they already be unconscious?