AGothika appears to be a word coined for this movie with little explanation of how it relates to the story. Numerous definitions have been created by fans of the movie, e.g., 'gothika applies to the loneliness of seeking answers without the belief and support of the people you depend on' or 'gothika is a situation in which someone sees or feels things that no one else does while those who don't think those thoughts see those who do as crazy, when they're not.' Neither of these definitions are verified by any published dictionary. Most likely, gothika is merely an affectatious spelling of gothica and is similar to other -ca words such as 'galactica' (things pertaining to the galaxy) or 'erotica' (things pertaining to erotic media). Thus, gothika can best be described as 'things pertaining to gothic styles,' as in architecture (i.e., the Woodward prison resembles a creepy gothic castle), art (the Anima Sola), the supernatural, the macabre, and preoccupation with death. Even the movie's photography, with its focus on blues and blacks, is suggestive of the dark and gloominess associated with gothic literature. Just for the record, the true Goths were East Germanic tribes who, in the 3rd and 4th centuries, warred against the Roman Empire and later adopted Arianism (a form of Christianity). In the 5th and 6th centuries, divided as the Visigoths and the Ostrogoths, they established powerful successor-states in the Iberian peninsula and Italy, respectively.
AChloe Sava (Penélope Cruz) killed her stepfather after years of abuse. She was also being raped while in the hospital, but all her ranting about Satan resulted in Miranda concluding that Chloe was delusional. After Miranda is admitted to the hospital as a patient, however, she actually hears the man raping Chloe and sees a tattoo of the Anima Sola on his chest.