A character is a person depicted in a narrative or drama. Characters may be flat, minor characters; or round, and major. The main character in a story is generally known as the protagonist; the character who opposes him or her is the antagonist.
A character is a person, or sometimes even an animal, who takes part in the action of a short story or other literary work.
I think Miss Brill is a static character due to how she does not undergo an important inner change. Throughout the story she, herself, doesn't change but her attitude/ mood does.