Prevent file deletion on server but allow read/write permissions

I'd rethink the requirements.

The literal answer is that yes, you can mark the files as being undeletable.

The access control list setting via the command line chmod command is something akin to the following:

chmod +a "groupname deny delete"

In practice, these same requirements do allow the shared files to be effectively deleted; via overwrite. (This is why the Unix-layer file protections don't bother to differentiate write from delete access.) These requirements also allow partial file corruptions, a situation which tends to be far more pernicious.

Further to our fearless leaders (MrHoffman) comment.

Some applications save new versions of a document by creating a temporary file, deleting the old file, and renaming the temporary file to the original files name. This will not work with file delete disabled. I would not be surprised if Microsoft Office was guilty of this.

It has been my experience that trying to mark stuff undeletable is a lost cause if files need to be modified. If they don't need to be modified then just make them read only.

I agree that your scenario doesn't make much sense.

First suggestion I have is user training + backups.

Another option (depending on what you are trying to acheive) is to restore the folders in question periodically to undo the changes.