People who were accepted into the ranks usually had been forbidden to have personal property. Free care was primarily for the indigent, not for the merely temporary disabled. And when religious institutions have cared for the children of the wealthy they almost universally did so for pay(yes the child is homeless, but assuming he is given his father's things he is also very wealthy).
And FFS, the OP said "Down syndrome" , not "autistic". I do not think highly of bringing modern classifications into the fantasy world, but he was consistent. You are conflating very different things.