It is possible for other computers to see your A drive - if you allow it -
but it sounds like you are editing a document directly off a floppy. Word
sometimes needs to create temporary files and it creates them in the same
folder as the document it is editing, so it is probably your computer
accessing your floppy drive. It is not a good idea to edit files from
temporary folders or removable media - copy the document to your hard drive
and edit the copy and then copy the edited document back to floppy.

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Enjoy,
Tony