The animal should not be a cloned beast, a genetic mutation, or a paranormal entity. Martians and vampires need not apply. At present, I will note a few trends that I've seen in cryptofiction, especially short stories. There are a few variations on this which show more depth. Sometimes there is a trophy, often there is none.
Man meets beast, beast disappears without a trace, man is left only with a story.
Man meets beast, man disappears leaving only a vague note. Gotta love those stories with a moral. Don't go sticking your nose into things that are better left unknown. Man meets beast, man befriends beast. There are different subcategories here, as well.