Ten years prior to the events of the game, Quote and Curly Brace were sent to the floating Island during the conflict over the Demon Crown. Unlike the other robots sent to the Island, Quote and Curly were ordered to destroy the Demon Crown rather than recover it. As they arrived later than the other robots, much of the Island was in shambles by the time they arrived, with destruction and carnage everywhere. By the time they found the Demon Crown, a human - Miakid - had already found it first and unleashed its power. Quote and Curly battled him and successfully wounded him but were eventually defeated, and were incapacitated for the next ten years, causing memory loss.
Curly Brace is significantly more vocal and outgoing than Quote, a fact that is much more apparent in Curly Story. She is bright and cheery, and expresses joy when lending a hand. Likewise, she is also affected by negative events, as she is seemingly very disturbed about the effects of the war 10 years before. She is fiercely protective of the people she cares about, going as far as to attack Quote to defend the Colons from harm. She is willing to sacrifice herself for the people she trusts, as shown when she gives Quote her Air Tank, allowing herself to drown in his place. Misery comments that she is almost as unrelenting as Quote in Curly Story.
Curly reawakens some time after the ten years from their battle with complete amnesia (remembering only her name). Somewhere in or near the Sand Zone, she stumbled upon four orphaned Mimigas called the Colons. She decided to take them as her adopted children and lived peacefully until the Doctor's minions began roaming around the Island, kidnapping Mimigas. Before long, Quote arrived in the Sand Zone, where he stumbled upon Curly and the Mimigas she's protecting. Curly mistakes Quote for a "Killer Robot" and attacks, but ends up being defeated. Upon seeing Quote spare her "children", she realized Quote was not trying to eliminate them.
Soon after Quote's departure, Misery arrives in the Sand Zone and teleports the Colons to the Plantation. She then sends Curly to the Labyrinth, where her injuries are treated by Dr. Gero, who heals her. She then strikes out for the Boulder Room, where she meets up with Quote. After a scuffle with Balrog, the two continue further into the Labyrinth together until they come across and defeat the Core. Water then fills the room, and Quote would have drowned, if Curly had not given him her Air Tank.
If Quote has the Tow Rope, he can save Curly. Curly can then be carried to safety and treated by Quote. Unfortunately, the two became separated upon Ironhead's defeat. If Curly is not re-attached to your back after saving her and you go to fight Ironhead, you will never be able to get back to her as the door leading to the waterway will be locked.
Curly later washed up in the Plantation, where she was found by Cthulhu. She had once again become afflicted by amnesia, no longer remembering even her name. Quote then found her, and traveled to the Mimiga Village Graveyard to find a mushroom to restore her memory - Ma Pignon. This restores all of her memory, including Quote's name (which she reveals for the first time in the entire game). Curly then gives Quote an item known as the Iron Bond. The Iron Bond's item description refers to Curly as "The only person you would trust your back to."
Curly appears once more in Sacred Grounds. Unlike all other times, she has the Nemesis, as opposed to her usual weapon, the Machine Gun. Quote straps her to his back with the Tow Rope and together they defeat Ballos. As Ballos dies, the walls begin to close in, but she and Quote are rescued by Balrog. The three of them then go and live together someplace nice.