I'm aware that is the current narrative of the game where the PC owes Bailey money for living in the orphanage for 'free'.
I wasn't calling it arbitrary because I don't like the idea, but rather that's what I describe their actions of taking advantage of the PC (and other orphans presumably) by extorting them like you said when it's likely not legal for them to do that, which could be borrowed over to the dormitory narrative I suggested.
I proposed my idea because I've gotten the impression that Bailey might actually have some sort of power over the town's officials that could prevent the PC receiving any help from the corrupted authorities, as implied from the Cafe Grand Reopening scene where Bailey made the mayor interrupted the PC from spreading the dark reality of the orphanage and dismiss it all as a joke.
		
		
	 
I always reasoned that while the town is relatively corrupt the reason why we dont go to authoritites is because we have absolutely no connection to rely on or to call up on.
In the dormitary example even if we were orphans we still got our official ID's which means that at any point we enter any official building and ask for replacement because even if they are corrupt i would only need to grease their gears a bit for my replacement.
Now with the orphange example we can assume that our ID's arent made yet, they need to be validated by the orphange to work. Bailey needs to confirm that we are of age, healthy, got our stuff back and really left the place with all paperwork done but he refuses to do that so officially we DONT EXIST yet. Even if we would go to the cops all they would do is call up Bailey and he would say that the ID's are still in making and that would be the end of it.
My impression on Bailey is similar to what
 RiloLaki said, but im more inclined to think that hes only keeping assets safe as only healthy slaves get to make good money and also hes probably still vary of some laws that could cost him much cash like us dying on the streets or losing our mind.