We can use tefillin and their accessories as a case in point.
The plastic, protective cover for my tefillin shel rosh broke and I replaced it. The question arises, does this broken plastic box have any holiness by virtue of it having housed my head tefillin (for many years). More specifically, does the broken plastic cover need to be buried?
Part of this question is: How far does tashmish kedusha extend? For example, does it extend to the tefillin bag or even to the plastic bag that I use to carry the tefillin bag? As to how it arises, a torah cover touches the klaf itself, but the plastic box touches only the outside of the tefillin, not the klaf inside. Does that mean the plastic cover does not have any tashmish kedusha? And what is the status of the 3"x4" mirror that is always in my tefillin bag?
I present these specific questions as a way of asking about the general principles of tashmish kedusha.