There are many clear parallels in the Lord of the Rings between the characters of Gollum and Frodo. In many ways, they represent two sides of the same coin. Their paths, or ultimately their downfalls, both start with them coming into possession of the One Ring, and then carrying it as an increasingly heavy burden across an extended period of time. However, the choices that they make, and the ways in which they interact with others ultimately leads them to two very different outcomes. For Frodo, the ring does consume him eventually, and he fails right at the last moment to drop it into the fires of Mount Doom and destroy it. However, he still manages to stay true to who he is at heart, surrounded by loyal loved ones, and he returns home to The Shire.
Gollum, on the other hand, shows the flip side of this path. He chose to isolate himself from the world rather than rely on friendship or loyalty, and subsequently the ring tormented him for years before eventually snapping his mind. Interestingly though, Gollum isn’t the only character that depicts the terrifying and devastating effects that a ring of power can have on its bearer, especially when the ring is suddenly lost, or betrays its wearer to go and find a new master. In fact, there are some extended edition scenes in The Hobbit films that show another poor soul who had been driven to madness by his years of exposure to a ring of power, and then the subsequent bereavement that he experiences when it is taken from him. That character is Thrain, Thorin’s father.
It is important to note that Thorin’s family, whether because they are direct descendants of the line of Durin, or because they are easily blinded by power and greed, already have a susceptibility to dragon-sickness. This is what causes Thorin to go against his word of helping the men of Lake Town, it is what causes him to board himself and his kin up inside the mountain rather than fighting honorably in the Battle of Five Armies, and it is what leads him to ruthlessly reject Bilbo, despite the hobbit only trying to help him. Luckily, Thorin does snap out of his dragon-sickness right at the end and manage to regain his respect, dying as a hero and a leader who will be remembered.
But it is important to keep in mind this history of illness in the family, when it comes to the extended scenes in The Hobbit trilogy where Gandalf goes into Dol Guldur and discovers a petrified and traumatized Thrain. It is difficult to say whether his mental state is due entirely to what he has been through at the hands of the enemy, or if it is in part his proneness to dragon-sickness.
However, there are some key indicators that suggest his mental state is a terrifying depiction of the effects of his ring of power. The scene at first takes on many references to other tropes, both within and outside of the Tolkien franchise. It is set up much like a horror film: the small hunched creature running through the shadows, the snarling noises he makes as he bursts forth into the light and then swiftly disappears again, the jump scare as he pounces on Gandalf and wrestles him to the ground. This automatically puts the audience on edge, and notifies them that something isn’t quite right, almost as if Thrain has been possessed.
This is the first hint that there is a dark power at work over his mind. One reason audiences might recognize this is because it is also another reference to the Lord of the Rings and the possession of King Theoden under the powers of Saruman, after Grima’s cunning plan to poison the king's mind. There are again obvious parallel between the two: the old, withered look; the way that Gandalf uses his hand to draw out the sickness of the mind and return the person to a state of peace. Perhaps most importantly, both of them, once they have gotten over the shock of what has happened to them, remember their respective sons and ask to see them.
It is then explained in a flashback scene that the terrible darkness that has come over Thrain’s mind and driven him mad (much in the same way it did with Gollum) is the loss of his ring of power. Azog is shown cutting the Dwarven ring, the last of the seven great rings given to Dwarven kings, off Thrain’s finger. Thrain has had the ring in his possession for decades, ever since it was handed down to him. It had helped him in many ways to govern his people, to be a great and noble warrior, and to make Erebor a rich and strong kingdom before Smaug came.
Therefore, when Thrain loses this ring, it catapults him to breaking point and sends him spiraling into the terrifying, shrunken version of himself that Gandalf finds in the dungeons of Dol Guldur. Once Gandalf has cleared the fog from his mind, he returns to himself, but only briefly, before he is whisked away into Sauron’s evil clutches forever.