I install limewire, download what I want then unistall. I find the longer you leave it on the slower your computer goes. As soon as you uninstall it will quicken up. When you uninstall run a search for limewire because it leaves loads of files behind.
As for your question. Mine go into the recycling bin unless I have deleted from limewires libary. If it's from the libary I don't know where they go. If you want to make sure they are deleted move them from the limewire folder into another and then delete them. You will see them in recycling then.