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!

- In-Game Description

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.