Throughout the book of “Harry Potter and the Half-Blood Prince,” we’re treated to a lot of flashbacks surrounding both the Horcruxes and Voldemort’s past, all but two of which are cut from the films (the only ones depicted on screen are Dumbledore meeting a young Voldemort at his orphanage and the aforementioned one with Slughorn). One that doesn’t physically involve Voldemort at all, because he’s not born yet, involves the Gaunt family, which is where we learn about a ring that once belonged to the ancient pureblood Peverell family that becomes a Horcrux later on.
When a Ministry official named Bob Ogden, who provided the memory to Dumbledore, goes to the rundown Gaunt house to investigate an attack on a local non-magical Muggle, he meets patriarch Marvolo and his two children Merope and Morfin. Morfin, as it turns out, did attack a local Muggle, and while Marvolo is hassling Bob over his investigation, he shoves a ring into the man’s face, yelling:
“See this? See this? Know what it is? Know where it came from? Centuries it’s been in our family, that’s how far back we go, and pure-blood all the way! Know how much I’ve been offered for this, with the Peverell coat of arms engraved on the stone?”
Here’s how things go for the Gaunts after this memory ends. Merope runs away with a wealthy and handsome Muggle named Tom Riddle, who leaves her after she stops dosing him with love potions; she gives birth to the future Voldemort and dies. Marvolo dies, Morfin picks up the ring, and Tom Marvolo Riddle, named for his father and grandfather, kills his uncle and steals the ring. So how does it become a Horcrux, and how is it destroyed? As Dumbledore explains to Harry in “Half-Blood Prince,” he took it for himself and paid a horrible price:
“The ring, Harry. Marvolo’s ring. And a terrible curse there was upon it too. Had it not been — forgive me the lack of seemly modesty — for my own prodigious skill, and for Professor Snape’s timely action when I returned to Hogwarts, desperately injured, I might not have lived to tell the tale. However, a withered hand does not seem an unreasonable exchange for a seventh of Voldemort’s soul. The ring is no longer a Horcrux.”
The ring did, however, contain a Deathly Hallow — specifically, the Resurrection Stone — which explains Dumbledore’s interest in it. Luckily, by the time Harry realizes it’s a Horcrux, it’s already destroyed.