When a hero is reduced to 0 HP, they are at "Death's Door."
While in this state, they will suffer stat penalties, plus any further damage has a chance to kill them.
Heal them to get off Death's Door!
Death's Door affects heroes when their HP reaches 0. At any time during this state the hero may die when damage is dealt to him; even if the hero would normally take no damage. It is thus advisable to attempt to heal any heroes on Death's Door before they die.