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. Sometimes there are escaped exotics, sometimes outright hoaxes, occasionally there are misidentifications.