Windows

Change the effective permission under the Advanced Security Settings.

To prevent a file from being deleted, you must ensure that the user is not granted the Delete Subfolders and Files special permission on the parent folder, explicitly or through group membership. To do this, use the Effective Permissions tab to view the folder's special permissions that are granted to the user. If Delete Subfolders and Files is selected, the user can delete all files within the folder.

To give the user access to the folder and its files without the ability to delete them, clear the Full Control check box and ensure that the user is not also granted Full Control via membership in another group. Although explicit permissions override inherited permissions, you cannot deny Full Control without also denying Modify, Read & Execute, List Folder Contents, Read, and Write. To prevent a user who is granted Full Control, by way of inherited group permissions, from deleting MyFolder and its files, you can do one of the following:

Explicitly deny the Delete Subfolders and Files special permission for either the group or for the individual user.
Remove inheritance from the folder and then reset the permissions for the group.
Note

Anyone who has List Folder Contents permission for a folder can view file properties on any file in the folder, even if file permissions prevent them from seeing the contents of the file.

Hope this helps

Do you want them to not delete the folders or the files they have in the folders?

And Fung's answer was technically correct.

Point value changed by question poster.

Hmmzz just give em Read/Execute/ and Write permissions to that folder. Make a new folder with the same subfolders and give em delete permissions here. Now just overwrite @ the end of the day. just an idea ;P