Here's what happened:
1. Dumbledore finds the ring: Dumbledore discovered the ring, a family heirloom of the Gaunt family, in a hidden compartment in the Riddle House.
2. He recognizes the dark magic: Dumbledore realized the ring was cursed and contained a Horcrux. He tried to destroy it by smashing it, but it did not break.
3. The stone's curse: Instead, the ring was only broken, and Dumbledore was cursed with a powerful dark magic that slowly drained his life.
4. The Horcrux remains: Dumbledore, even after being cursed, was able to successfully remove the stone from the ring, effectively separating the Horcrux from the object itself.
While the ring was broken, the Horcrux remained inside the stone. It was later destroyed by Harry Potter using the sword of Gryffindor.
It's important to remember that the Horcrux is not the ring itself, but a piece of Voldemort's soul, and it can exist in any object. Dumbledore's actions did not destroy the Horcrux, but only separated it from the ring.