When the user tries to delete a folder, they will be prompted to send the tests into the Unattached folder. The problem is, they are still able to delete the individual tests without being prompted to send them into the Unattached folder. I suggest going into the Groups and Permissions and disabling the deleting capabilities for all users except those who should be allowed to delete the tests. In order to do this, you will need to create a custom user group, as the permissions for the default user groups can't be changed. Once you have created the custom user group, you will need to add the users to that group and remove them from the default group, as leaving them in both groups will most likely cause issues within ALM.
To do this, access Groups and Permissions in Project Customization and click the 'New Group' button. In the 'New Group' dialog, you will enter the name of the custom group, then select one of the current user groups from the 'Set As' dataset, which will create the custom group containing the same permissions as the default user group you have selected from the dataset. To the right of the user groups, you will select 'Permissions', then 'Test Lab' or 'Test Plan', or any other module you would like to edit permissions in. You may need to scroll right depending on the number of modules you have displayed. In that list, you will find the permissions. There you will be able to change what the users are able to do within the ALM modules.