Wera,
How many days do you have your Saved incomplete songs saved for? Set it to 0 so you can delete the songs for good once you shut down Limwire.
Go to: Tools/Saving/ and where is says: Days To Keep Incomplete Files, put in 0. Click Apply and hope that solves this problem.
Next, goto Library and click on Incomplete Files and hilight all the downloads and delete them for good!
Let us know if that helps you.