Using the serpent's strike special ability of the feat Animal Devotion (Complete Champion 54-55), it's possible for a character to get for at least 1 minute 1/day a bite natural attack that deals only 1d3 Constitution damage (and no--not 0--hp damage). Does the feat Improved Natural Attack (MM 304) increase this Constitution damage or does the feat Improved Natural Attack only increase hp damage dealt by a natural attack?
In this case the feat Improved Natural Attack appears to increase the Constitution ability damage dealt by the serpent's strike, but it's really difficult taking the feat Improved Natural Attack (bite) if this special ability is one's only bite attack
The feat Animal Devotion (Complete Champion 54-5) as one of its benefits says that when a creature with the feat takes a swift action the creature can gain the following special ability:
Serpent’s Strike: You gain a natural bite attack that deals 1d3 points of Constitution damage but no hit point damage. A successful Fortitude save (DC 10 + 1/2 your character level + your Cha modifier) negates the Constitution damage. Creatures immune to poison are immune to this effect. Your upper canine teeth grow into fangs when you activate serpent’s strike and remain in that form as long as the effect is active.
The feat Improved Natural Attack (MM 304) says as its Benefit that
Choose one of the creature’s natural attack forms. The damage for this natural weapon increases by one step, as if the creature’s size had increased by one category: 1d2, 1d3, 1d4, 1d6, 1d8, 2d6, 3d6, 4d6, 6d6, 8d6, 12d6. A weapon or attack that deals 1d10 points of damage increases as follows: 1d10, 2d8, 3d8, 4d8, 6d8, 8d8, 12d8.
Thus a creature with the feat Animal Devotion who gains enough XP to advance to a level while he has the serpent's strike special ability active could take the feat Improved Natural Attack (bite) to increase the damage dealt by that natural attack from 1d3 points of Constitution ability damage to 1d4 points of Constitution ability damage. The creature's timing and math need to be perfect, however, as the creature doesn't meet the prerequisites the feat Improved Natural Attack (bite)--and therefore can't pick the feat--if the serpent's strike ability isn't currently active.
Obviously, if the creature can constantly make a natural bite attack in addition to being able to activate serpent's strike, taking this feat is much easier.