Bag End still stands as one of the most iconic homes in all media, with Bilbo Baggins' journey beginning in the cozy Hobbit hole and Frodo's journey ending there. After the events of The Lord of the Rings, each Hobbit from the Fellowship returned to their day-to-day lives in the Shire. But Frodo could never settle down, and eventually left into the west for the Undying Lands, never to return. So, without anyone at home, what became of his house under the hill?
The opening of The Hobbit reads, "In a hole in the ground there lived a Hobbit. Not a nasty, dirty, wet hole, filled with the ends of worms and oozy smell... It was a Hobbit-hole, and that means comfort," which perfectly sets the scene for Bilbo's life. He lived in one of the comfiest places in Middle-earth but still yearned for adventure. The same need would later be felt by Frodo, who left Bag End to take the One Ring to Rivendell.
After The War of the Ring, the Shire was left ravaged and destroyed. Peter Jackson's adaptation left the Shire alone, thinking that it would make for a depressing ending if it were destroyed. But in the books, the land didn't fare nearly as well. After Frodo and Co. left, Lotho Sackville-Baggins took over Bag End and began trading crops with Saruman, which eventually led to Saruman taking notice and claiming the territory, burning and industrializing much of the land.
Upon returning to the Shire, Frodo and his allies led the Hobbits into the Battle of Bywater. After claiming victory, the Shire was made free once more, and Saruman was killed on the porch of Bag End. Lobelia would then return the home back to the Baggins, trying to make amends for her family's wrongdoings. In the years after the battle, much of Hobbiton was rebuilt and regrown with the help of Samwise Gamgee's gardening skills. However, despite feeling like home again, Frodo never could relax, and he eventually decided to leave with the Elves for the Undying Lands. With his departure, he handed over ownership of Bag End to the Gamgee family, which was a big step-up from Sam's original home.
Samwise went on to have 13 children with his wife, Rosie Cotton, and they all lived in Bag End. The Hobbit hole was eventually passed down through three generations of the Gamgee family, only now, they were referred to as the Gardeners of the Hill -- a name they claimed in honor of Samwise replanting much of the Shire. Samwise would also follow in his friend Frodo's footsteps and leave his home for the Undying Lands.
So, after Frodo took his leave, the last thing known about the Shire is that the region prospered and the Gardener family lived on and maintained Bag End, which is a fitting ending for a home that it represented so much of the good in the world.