Given that the game is moving away from its questionable origins, they might as well embrace that new narrative.
I think I like the idea of that better where the PC is renting for their accommodation to study which is a trap set up by Bailey who has deviant plans for those who couldn't pay up and has no interest in simply evicting them, as opposed to the PC being supposedly a young adult still living in an orphanage and having to pay off their arbitrary debt to Bailey.
I would say its better if we dont do that because it still puts an emphasis on why its soo shitty for us right now.
We are living in the orphange not because we are underage but because the headmaster is extorting money from us in a kind of slave labor fashion. We are forced to stay there and pay or we dont get our IDs back, it just makes more sense for this to be the case because the dormitary would just be weak and run into the logical issue on why exactly couldnt we just get into the police and report the issue, call officials and such.
With us being orphans who lived without family and anybody who would have helped us it makes more sense why we couldnt get help from officials. We know no one, had interacted with the goverment zero times and are powerless to change things.
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You enter Bailey's office. "I know why you're here," she says, running a hand through her dark hair. "You want me to release you from my protection, so you'll be an independent citizen. I could do that. But there's a problem. You've been living under my roof without giving anything in return. You owe me. Until you pay me back, I'm not letting you go."
She lifts an envelope from her desk and thumbs through the contents. You glimpse your name. She smiles as she hides your identification documents in her jacket. "£100 should do. To start with. I don't care how you get it. Knock on doors and ask for work. Rent yourself as a footstool. Steal it even. Just have it a week from now. Or I'll find a way to extract value from you."
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As for the school, it doesnt matter what we call it. It could be aswell a trade school or high school also. It doesnt need to be a university infact it also gives a nice note to your situation if we imagine it as its just some public school with no name to it.