Final answer:
Eurynome's advice to Penelope is not directly found in the provided texts, but is likely related to advice about remarrying, which Penelope ignores as she waits for Odysseus.
Step-by-step explanation:
The advice given vainly to Penelope by Eurynome is not explicitly detailed within the provided texts. However, considering the context of works related to The Odyssey, one might infer that Eurynome's advice would be similar to the counsel often given to Penelope in the epic: to remarry and move on, assuming that her husband Odysseus would not return. Since Penelope maintains her faith in her husband's return, advice to the contrary would be in vain.