Menu rings are unsigned so you can't set it to -1 as one would do for a listbox e.g.
If you want to do this with a menu ring, you could add an entry as option 0; it could be empty or be named "No file selected"...e.g. That way you'll detect the change. OR you could check the value when the control reports a mouse or key event instead.
I normally use a standard menu for this, have the last opened files available in a section under a File menu, just as typical in other applications (including LV).