Once your .Mac account has expired, the iDisk will remain on the Desktop. I tried getting rid of it, to no avail, until I was instructed by .Mac support to explicitly remove my name and password information from the .Mac System Preferences pane.

Note that once your iDisk is deactivated as described above, you get an image with whatever was stored on it; you are free to copy or delete that data as you wish.

Hope this helps someone else; the solution was not obvious to me.