are you sure your user isn't able to recover their deleted files?
Go to the user options icon on the menu bar at the top of the alfresco screen ( it is to the left of the hide-show side bar option )
Then scroll down to management and select "manage deleted items"
I was able to recover files that i had deleted from here and either choose to restore them to their original location or restore them to another location.
I'm currently playing with the enterprise version of the product to find if it meets our needs.
Users with collaborator permission on a space don't seem to be able to delete files ( but can add them ).
Users with co-ordinator permissions on a space can delete files as well.
The exception seems to be if the user with collaborator permission is the OWNER of the file in which case they retain delete permission. So if you really wanted to stop your collaborator users deleting their own documents you could get a co-ordinator to seize ownership of the documents after creation.
I'm sure others will be able to suggest some other approaches that i haven't discovered yet.