A given output of damage in a reduced time frame. Meaning it checks that party members have been healed in between.
The one I remember best is Kefka where it would bring HP to 1, make people unable, an only give a few seconds to top people up before a raid wide.
White hole in ExDeath is arguably a heal check too, you had to Max everyone quickly, after a mechanic where people were running around.
Maybe the adds you had to heal to full during Shinryu Ext too.
I don't see strict healing checks in Eden, more like continued healing requirements... maybe the flares into share on Voidwalker... I haven't tried Titan though.
