It's a long story, perhaps you should better read the book. Briefly, Regulus replaced it (in the cave where Harry and Dumbledore found the fake horcrux), told Kreacher to destroy it, but it couldn't be destroyed. The locket got stolen by Mundungus, later it was confiscated by Dolores Umbridge, who kept it for a while. Near the beginning of the seventh book, Harry and his friends must find a way to steal the locket from the ministry, which is now under the control of Lord Voldemort.
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The fake locket Dumbledore died to obtain in Harry Potter & The Half-Blood Prince.
Horcrux #1- the diary, Harry Potter destroyed using a basilisk fang Horcrux #2- the Gaunt Ring, killed by Dumbledore Horcrux #3- the Slytherin locket, killed by Ron Weasley with the sword of Godric Gryffindor Horcrux #4-the cup of Hufflepuff, killed by Hermione Granger by a basilisk fang Horcrux #5- the diadem of Rowena Ravenclaw, killed by Harry Potter by a fire in the Room of Requirement Horcrux #6- the snake Nagini, killed by Neville Longbottom by the sword of Godric Gryffindor Horcrux #7- Harry Potter, killed by Lord Voldemort by the "Avada Kedavra" killing curse
Lord Volemorts horcruxes included: - Tom Riddle's Diary - Slytherin's locket - The ring - Helga Hufflepuffs cup - The diadem of Rowena Ravenclaw - Harry Potter - Nagini the snake
Nobody because Horcruxes don't exist and this particular Horcrux is mentioned in a parody of Harry Potter called; A Very Potter Musical.
I highly doubt it. Dementors are only mentioned once or twice in general in Deathly Hallows (the most memorable mention is during the Horcrux search when Harry couldn't conjure a Patronus because of Tom Riddle's Horcrux locket) so the chance they would be in the trailer is very small.