" Nothing is easy in home repair!!!
We tried to replace the packing washer in our outside hose bib and that
seemed to go OK, but we removed the screw securing the handle and that
screw seemed to plug a hole in the hollow stem which now leaks. What is
the purpose of a hole in the hollow stem and how do you stop THAT from
from leaking? The guys at Lowes never heard of such a thing. Here is a
picture to help you understand what I have...
http://mysite.verizon.net/bjkass123/bibhole.jpg Thanks for any ideas of
what it's for and how to fix. Joy"

I've also never heard of a completely hollow valve stem. Usually, the hole
is tapped only deep enough to take the handle mounting screw. Are you sure
it is leaking through the hole, and not from the base of the stem where it
goes into the valve nut? May be easiest just to replace the hose bib valve,
if replacing the packing and replacing the handle does not do the trick.
Bib valves are fairly cheap.