I know that this might be a duplicate question, but I have not found any satisfactory answers that clear up my lack of understanding. Here is my question. Say a sloth hangs on a tree in the middle of nowhere. Therefore, he has some gravitational potential energy $mgh$. Next, say he falls to the ground. From the work-energy theorem, there was no net work done on him, since the his initial velocity was zero and his final velocity was zero. Therefore no energy was transferred, since there was no net work. However, now that the sloth is on the ground, there is no more gravitational potential energy, meaning that there is less energy in the system than there was initially. This seems to contradict conservation of energy. Obviously, I am making some form of conceptual error, but I am not sure how.
Conservation of energy, as you note, holds for "the system." For instance, if you push on a ball, that ball gains energy, but the energy of the ball is not conserved--only the energy of you and the ball. In this case, the system needs to include more than just "the sloth" because the sloth is not an isolated system--there are external forces at work. Here, the main one is the ground, which does work on the sloth. The sloth exerts a force on the ground, and some vibrations go off into the surrounding area, which are eventually damped out by friction and turn into heat.
What I'm saying here is that, if a sloth falls in the middle of the forest and nobody's around to hear it, it has to make a sound--by conservation of energy.
There is an external agent that removes mechanical energy from the sloth, namely the normal force exerted by the ground. You are right that no net work is done, but remember it is the work-kinetic-energy theorem: The net work equals the change in kinetic energy of the sloth.
When the sloth starts falling, it's potential energy starts getting converted to kinetic energy, and just before it hits the ground, all of its potential energy has been converted to kinetic energy. Now, the problem you're facing is because of the fact that you're considering just the sloth, which is wrong, because the sloth is interacting with the ground in this case, so with its kinetic energy, the sloth is hitting the ground, with some force. The energy the sloth has is utilized in its interaction with the ground, as in it gets converted to sound energy, heat energy and friction, and all the other forms of energy associated with the interaction. So the energy is conserved.