Philemon is a figure in Greek mythology. He and his wife Baucis offered hospitality to the disguised gods Zeus and Hermes when no one else in their town did, placing all of their meager resources at their guests' disposal. As a reward for their kindness, they were granted a wish. The couple asked that neither of them would have to outlive the other. When their natural lives drew to an end, they were transformed into intertwined trees. This story is most notably recorded in Ovid's Metamorphoses.
One of Ovid's stories in his book Metamorphoses is entitled "Baucis and Philemon." It's about a couple (Philemon is the man) who desire to not witness each others' death, and as a result, when they die (at the same time), they transform into trees. An incredibly beautiful story, in my opinion.