I like the way you think! Unfortunately I haven't this far seen any way to pay rent for the old lady in the first place.
Using first someone's pure generosity to then collect rent from subtenants sounds to me exactly like something the House Carozza would do, but perhaps I am just unaware of some finer details of the rental systems of Ikaanos.
Please tell me exactly how you rent houses from old ladies if you will, so I could perhaps do the same in my own game.