In the novel Hallowe'en Party, Miss Emlyn is the headmistress at the The Elms at Woodleigh Common. She is, according to Superintendent Spence, of the the few who had lived in the village for a very long time. Furthermore, the headmistress, she made it a point to know her students as well as their family backgrounds. Thus, although she was not present at the halloween party where Joyce Reynolds was murdered, it was natural for Poirot to turn to her as a resource person.
On Joyce's claim to have seen a murder long ago, Miss Emlyn tells Poirot that Joyce was a compulsive liar, one who boasted in order to impress those around her. On the other hand, Miss Emlyn did not think she had made everything up. She probably did witness something and then worked it up into some impressive happening that passed as a murder.
Nonetheless, Miss Emlyn is committed to the cause of justice and directs Poirot to speak to one of her teachers, Elizabeth Whittaker whom she believes might have seen something indicative at the halloween party.
Towards the end of the case, Poirot calls on Miss Emlyn again. By this time he has formed a definite opinion of who the criminals might be, but, unusually for him, he also wants to test his conclusions with Miss Emlyn. Various people in the village had said much the same thing to him: that if anybody has an idea who did the killing,Miss Emlyn would. Miss Emlyn admits to Poirot that she does indeed have a definite opinion but she would not be prepared to share it, presumably because it is an opinion formed without firm evidence. Earlier she had used the word "hunch" but Poirot believes her opinions go futher than that. To circumvent her reticence, Poirot offers to write four words on a sheet of paper. Miss Emlyn told him she agreed with the first two words but the next two is more difficult because she has no evidence and in fact the thought had not entered her head. Her response proves enough for Poirot to get on to lay out his conclusions to the authorities.
Miss Emlyn is a very old friend Honoria Bulstrode, the headmistress at Meadowbank School for Girls. Miss Bulstrode had apparently told Miss Emlyn about Poirot. Her words to Poirot about Meadowbank still being a school of distinction, spoken in the present tense, suggests that Miss Bulstrode had lifted the school turned the school around from the setbacks encountered in Cat Among the Pigeons.