It sounds like what you are asking about is an omniscient narrator. The omniscient narrator does not exactly become every character, but he or she is all knowing and can therefore see into the lives of each character, therefore giving the reader a more universal point of view.
Charlotte Perkins Gilman's story, "The Yellow Wallpaper" has an unnamed narrator who writes in the first person, so the point of view can be either third person or first person. But, as mentioned in the previous post, the anonymity of the narrator provides the reader the opportunity to relate to this narrator. In Gilman's story, for instance, the unnamed narrator could be any new mother of the Victorian Age who suffers from post-partum depression.
I agree that you really need to determine what perspective the narrator is speaking from before you try to put a term with it. The previous editors have explained the different points of view, so let us return to the discussion of the every man character....
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