The hadith literature treats haya as an interior quality and places it inside faith rather than beside it. A well known report counts the branches of faith and names haya as one of them; another states simply that haya is part of faith; a third, often quoted and often misread, says that if a person feels no haya then let him do as he wishes, which the commentators explain as a warning rather than a permission, on the reading that the loss of the sense of restraint removes the last internal check on conduct.
Because it is a disposition, the sources describe it as something a person can have towards God as well as towards other people. Feeling haya before God means conducting oneself in private as one would in public, and a good deal of the ethical literature builds on that reading rather than on any rule about clothing.
The Quranic instruction most often cited in this connection is the pair of verses telling believers to lower their gaze and guard their modesty. The order in which they appear is worth noticing: the instruction is addressed to believing men first, and to believing women in the verse that follows. The classical commentaries take this as establishing that responsibility for the conduct of a mixed public space is shared, and modern writers within the tradition frequently return to the point when the discussion narrows onto women alone.