Well that is odd! The only thing then that comes to mind is perhaps there was an issue with something not being fully stopped before moving the folder.
Local stores things in a few places. The uninstall document is probably the best resource for seeing where these are located, but as a summary those locations are:
~/Local Sites/- Default location of the WP site files./Applications/Local- The default location of the files for the Local app, for example, all the code needed to run the GUI part of Local~/Library/Application Support/Local- The config folder. Contains user settings as well as things like the “run” folder which is basically where things like the raw database files are located.