Daredevil card text is :
Response : After Daredevil thwarts , deal 1 damage to an enemy.
Part of CONSEQUENTIAL DAMAGE definition is :
After an ally thwarts , it takes consequential damage equal to the number of pips beneath its THW field.
I am almost sure that when there is only 1 life remaining on Daredevil he can't use his response. How can I justify that by the rules unless I say consequantial damages are not optional ?