Living Death when, popped, puts a buff on you. If you would die while this buff is up, you instead are healed to full and get a debuff. If you are not topped off by a healer (I don't quite understand the mechanics on this part, seeing as you're at full health once it activates - maybe you need to be overhealed?) before this debuff expires... you die.
If you do not actually die while the buff is active, it fades and the effect (and cooldown) is wasted.
And yes, I would figure Convalescence WOULD help with dealing with it... but it's still very much on the healer to heal/overheal you in time so you don't drop. The times I've had to use it have usually been in situations like I'm in a crowd of mobs and the healer was DPSing instead of healing and the like... and so even after healing to full I'm almost immediately dropping in health again - usually too far for the healer to "top me off" before the debuff countdown finishes.
If you do not actually die while the buff is active, it fades and the effect (and cooldown) is wasted.
And yes, I would figure Convalescence WOULD help with dealing with it... but it's still very much on the healer to heal/overheal you in time so you don't drop. The times I've had to use it have usually been in situations like I'm in a crowd of mobs and the healer was DPSing instead of healing and the like... and so even after healing to full I'm almost immediately dropping in health again - usually too far for the healer to "top me off" before the debuff countdown finishes.