If you make changes ONLY to the published arc, it does not update the local copy.
If you unpublish an arc, and don't have the local copy, your copy is gone (unless you had it autosaving.)
The local copy has no effect on unpublishing an arc.
Basically, before you unpublish, do a quick "Save as" so you DO have a copy, and give it a unique name. Otherwise, it's gone if there's nothing local.
Edit: Examples, just to make sure I'm being clear.
I write a story arc, "The Legend of the Legendary Legend." I test it, decide I like it, and publish it. As I publish, the two copies are exactly the same - the published version and the local, which I'll call legend.storyarc (.storyarc being the file type.)
I then get a tell, "Hey, you misspelled such-and-such, and this dialog was broken." I go to "My published arcs," and hit "Edit." ONLY the published version is edited. The local copy still has the typos and problems.
I decide I need to throw in an EB in a mission. I edit the published copy, adding "Defeat a boss" with my EB. The local copy is not changing in any way, shape or form.
A month later, I'm in a rush. I intend to unpublish "The Story of Frank the Chicken," but accidentally unpublish the "legend" story. Oops! I go to "My local stories," find the Legend file, and re-add it - but it still has the old typos, and doesn't have the EB. I have to re-edit it.
Now, what I *should* do at this time is re-edit the published copy and re-add it. Republish, which pushes your changes to the server. THEN go back in to Edit, pick Save As... and give it a name like Legend-Update.storyarc.
With me so far? When I do that second save, I now have a local file that's the same as the published file, with updates.
Now, another month goes by. I clean out m hard drive, moving files to CD, including the .storyarc files. I clean out the folder. Then I unpublish "Legend." I *cannot* republish it, since the file is no longer on the hard drive. I can copy it back over from the CD, THEN republish it - but if I don't do that, the story arc is gone for good.
Also, unpublishing and republishing resets any and all ratings, so if you had a 500 play, 5 star arc, unpublish and republish... you now have a 0 play, 0 star arc.
That help, or is it now clear as mud?
Thanks so much Bill!
I think im following you. I need to go and save the published arcs in order for them to be around when i unpublish them, If i want to save the changes i have made. otherwise all i will have is my local arcs. 
Right.
And when working on them... *Always* make backups, don't rely on autosave! (Autosave makes an autosave.storyarc file - but always overwrites it to make the new one.) I'll tend to save on each mission I make in an arc.
Seeing as how Bill didn't do it, I will.
MA Tutorials - An extensive Mission Architect tutorial, written by the poster above. 
*toots horn for Bill*
Thanks. Just wanted to answer the specific questions... since that's a lot of reading.
Indeed it is, your post above is a great synopsis of the publishing/un-publishing process though. I'll have to save it.
I find it easiest to think of it this way: I start with a copy of the file on my local computer. "Publishing" means copying that file to NCSoft's computer. I can either edit my copy or edit their copy, but an edit made on one is not reflected on the other. "Unpublishing" just means deleting the file from their computer.
It would work the same way if we were talking about Excel files or something instead of mission arcs.
Avatar: "Cheeky Jack O Lantern" by dimarie
When you post an arc, you have a local copy and a published copy. They are identical when you first post the arc.
What i'm trying to find out is when you make changes to the published arc only, what happens when/if i decide to unpublish this arc?
Does it replace/overwrite the local copy? or does the local copy remove all the changes back to where the local copy is saved?
Also can I delete the local copy and still unpublish an arc?
Thanks for the help,
Dementus