Even dragons have their ending.
It is no great surprise that Hobbits had a saying through which Bilbo could remind his companions that nothing lasts forever, since it is the Great Message: the lesson which every new generation must learn from their forefathers. Nothing is perpetual, however strong, secure, or inviolable it may appear.
All things come to an end.
But the second great message that all - Hobbits, Dwarves, Elves, and ourselves as well - must hear from those who have gone before is that we are the inheritors of their legacy, and that, through us, their stories continue.
Bilbo's story turned out not to be only his, since it was inherited from the Bullroarer, the Old Took, and even Gollum, Isildur and Sauron. And when Bilbo's part was played it became the story of Frodo and Sam, of all the future inhabitants of Bag End, and of all the future readers of the Red Book. Which means us.
Roads go ever ever on.
All things come to an end, and yet the Road goes ever on.