Any Facebook Like's are counted toward the URL they were clicked on. If you change your URL structure, you will lose the Like count as they will still be associated with the 'old' URL.
You can implement a Like button that 'points' to the old URL by implementing the JFBCLike module or adding the JFBCLike easy-tag, like below:
{JFBCLike href=http://www.site.com/old-url-here}
The problem with that is that when clicked and posted to a user's Timeline, the old URL will be shown and what user's will go to. If you have proper redirects setup, that should be ok, but it's on more thing to manage as time goes on.
I hope that helps explain, but if you have any other questions, just let me know.
Thanks,
Alex