What's up with The Rotten?
Solution 1:
Text in italics is directly from the collectors edition guide book.
As with any lore-driven question this is completely speculative and is my personal opinion based on the Guide Book, Item Descriptions, and leaps of faith I make, take all of this with a grain of salt.
Deep within the earth beneath Majula lies an anarchic settlement of filth and chaos built by the forsaken souls cast into The Pit.
At the bottom of the pit is The Gutter, a half put-together shantytown (resembling Blighttown from DSI) that is very dark, and very full of poison. We know that Aldia used this to throw his unwanted experiments in, and many kingdoms in the past have used the pit as a garbage dump. Many of the enemies in The Gutter and Black Gulch are remnants of Aldia's experiments, the Hunting Dog is born from the experiments conducted by Lord Aldia, and the Corrosive Ant Queen's presence in The Gutter seems to suggest that it began its life in the laboratory of Lord Aldia's mansion and eventually outlived its usefulness.
So the creatures in the Black Gulch are failed experiments. Really the only thing we can know for sure is that The Rotten is an amalgamation of these lost souls in the Gutter that have made their way to Black Gulch. We know that The Rotten absorbed so many life forces that he came to possess a Wondrous Soul of his own, which explains how he has a Great Soul.
Anything more than this is dedicated lore.
There is speculation that The Rotten is Pharros the Vagabond but even this theory takes some lore leaps. Also unexplained is the NG+ 'Old Dead One Soul' that may be a nod to Nito, with it's obvious visual parallels to The Rotten (This soul creates the Crypt Greatsword, which could be further evidence to a Nito connection). Further lore connections can be made by the central location of Hexes found around him, a possibility that Navlaan was cast down the pit when he was outcast from Majula. Finally, the surviving Giants guarding the Forgotten Key, remnants of the war in which you traverse in the Giant memories.
As for everything in the Souls Series, there is no clear cut answer, only vague correlations to descriptions and dialogue in game.