As was established by DavidW, and accepted by RetroGremlin in the comments, "The Vampires Who Loved Beowulf" by Mary Caraker.
The aliens are a dark-dwelling species who recreate their oral histories; the humans offer new stories as trade, among them Beowulf. Humans die in the recreation before the researchers realize what's going on and change which stories they offer.
According to Caraker's entry in The Encyclopedia of Science Fiction:
US author of whom relatively little is known; she is of Finnish descent and began to publish sf when she was nearing 50, with "The Vampires who Loved Beowulf" for Analog in January 1983, a story which makes up part of her first novel, Seven Worlds (fixup 1986), whose protagonist, a tough female Space Exploratory Forces agent named Morgan Faraday, is entrusted with the task of improving Communications between humans and other species. Its Young Adult sequel, The Snows of Jaspre (1989), places the same protagonist into a political and ecological crisis on the eponymous planet. Water Song (1987) and The Faces of Ceti (1991), singletons, likewise examine planets in crisis: the first a world, whose surface is almost all water, which faces an Ecological crisis; the second, a planet in dire need of food. I Remember, I Remember ... (1991 chap), a novella, recounts the sensations of a woman who awakens on a "coldship" without any memory of how she entered Suspended Animation.