Join the zoo of inevitable demise

The world is not the happy safe place some people like to think it is. Humans aren't the only ones who can contract terrible, terminal, and life-affecting illnesses. The animal kingdom is subject to a plethora of diseases, each one more depressing than the last. If you are an animal with a horrible illness, you are welcome to join our zoo. We can't cure your ills, but we can all laugh at you about it. And isn't laughter the best medicine?

To be in the group, you must have
1. A name
2. A horribly depressing disease
3. An animal
4. It must be unique from everyone else's