Oates has stated that she had the "Death and the Maiden" folktales in the back of her mind as she wrote this story; she even considered "Death and the Maiden" as a title.
A common motif in Renaissance art, the "Death and the Maiden" trope has origins in the Greek myth of Persephone and Hades. Persephone, the daughter of the goddess Demeter, is ensnared by Hades and doomed to live with him in the underworld for six months of the year. This myth is taken up as a larger allegory about the confrontation between love and death. (Check out this link for more.)
Oates may also have had in mind Franz Schubert's famous song "Death and the Maiden," in which Death poses as a "friend" to the maiden, who pleads with him not to "touch" her. "[The] story is clearly an allegory of the fatal attractions of death (or the devil)," Oates explains. "An innocent young girl is seduced by way of her own vanity; she mistakes death for erotic romance of a particularly American/trashy sort" (source). But it's only when Connie confronts Death (i.e., Arnold Friend) that she's able to move beyond her superficial values to something higher, to "heroism."