Tribble Carcasses are the remains of a Common or Uncommon rarity Tribble eaten by the [Cannibal Tribble]. Cannibal Tribbles have a chance of being rewarded for 
Assignment: Confiscate Contraband From Crew, but can also be bred by feeding [Baked Tribble] and [Tribble Kebab] to common or uncommon tribbles.
Ten tribble carcasses are required for 
Assignment: Tribble Bounty, which rewards 1000 
amongst others.