Tower of Remnants is one of the College's towers that houses various rare items (animals, herbs, minerals, objects) as well as continuously emitting magic. This tower is usually off-limits to the students, but opportunities exist to enter the tower while supervised to pick up some part-time work.
The tower is full of items that cannot be disposed of. For example, failed items that were created by alchemy/sorcery. Extinct or endangered species are located here as well. It is also special since it can mimic the environments of various areas around the world where valuable minerals and herbs can be found, enabling these precious items to be gathered at one location. The part-time work is usually collecting these minerals and herbs.
The tower also serves as a shelter for Sorcerers who caused issues throughout the world outside of the College. They agreed to stay at the College in this tower to avoid being killed or to continue working on their sorcery. Fabio is one of these people.
We first see the entrance of the tower at the end of chapter 67 when Lucy announces she will be entering it for some extra money to pay for her tuition. In chapter 68 the students enter the tower together on the night of Halloween since special plants and minerals can be gathered on that day.