Meant as an "innovative school to educate tomorrow's elite", the Institution was only accessible to those who could pay for its ludicrous entrance fee. For most people in the Sky City, it was the place one would try to attend if planning to get into politics in the future. Scholarships were incredibly sought after.
The other, lesser known way to get into the Institution was to be an Anomaly.
Anomalies were generally hunted down by Inner City Security, but those lucky enough to be born to influent families were usually sent to the Institution's Special Education Program. Rarely, Inner City Security would also send a few Anomalies to the Institution under the Rehabilitation Program.
Of course, the fate of an Anomaly in the Institution was to conform to its teachings and become a key part of the system that aimed to destroy them entirely. If one would not, or could not conform, they would have the same fate as any other Anomaly : death or experimentation.
Students in the Special Education Program were usually separated from their "normal" peers, including in dorms.