Symbolism, Imagery, Allegory
Snakes get a pretty bad rap in literature, and this myth is no different. Whether they're corrupting Eve in the Bible, killing Cleopatra in Shakespeare's play, or trying to vanquish Harry Potter in the Chamber of Secrets, literary serpents are a nasty bunch.
These serpents are associated with sneakiness, a corruption of innocence, and quick deaths. And, yep, all three of these ideas play into Eurydice's unexpected demise. As she runs along a riverbank, a hidden snake bites her without warning (sneaky!), instantly robbing innocent Eurydice (innocence!) of her life (quick death!).
Don't forget where the snake bites Eurydice: on her ankle. Throughout Greek mythology, ankles and heels appear as a symbol of vulnerability. Achilles' only weak spot was his heel, and young Persephone was known for – of all things – her "beautiful ankles." So the fact that the snake bit Eurydice on the ankle might mean that, symbolically, it went for the young lass' most vulnerable, exposed body part. Or it might just be that, since this was a snake on the ground, Eurydice's ankle was the easiest part to reach. (We like the first explanation better.)
Vladmir Nabokov's short story, "The Return of Chorb," which draws heavily from the Orpheus and Eurydice myth, also uses some fun snake-like imagery: when Chorb and his wife are on their honeymoon, his wife touches an electrical wire that kills her. We're pretty sure the electrical wire serves as a modern stand-in for a snake. Stay away from both!