Not all foods are best served fresh. This fruit has seen its best-before date a long time ago, but that only makes it more valuable. Rotten Apples are a great source of aggressive contaminants with which to coat one's Aluminium Bolts or Aluminium Arrows. Very useful for when the prey just has to die. If absolutely necessary, Rotten Apples can be consumed for a small 6% refill of the Hunger bar.
Using Crafting, Rotten Apples will give arrows and bolts a poisonous coating. When a living target is struck with anything with poison, it will slowly but surely die, unless the target happens to down Antibiotics pills, or use an Antiseptic Bandage. As these can be rare on Orca Island, the likelihood of making a guaranteed kill is high. To further hasten the target's demise, Rotten Apples can be used in more complex recipes to create even deadlier ammunition.
Apparently the people who eat apples on Orca Island are a forgetful bunch, as this late delicacy can be rather commonly found all around, with the most likely spots being kitchens, gas stations and supermarkets.