To my knowledge, the answer to this is no, can't be done, but I need a second opinion:
If I have the following:
<li>
    <a >#</a>
    <div class="sub">
    #
    </div>
</li>
and have a background image that appears on li a:hover is it possible to have that background stay on when hovering on the .sub div? This also has to work pure CSS - no javascript cheats.
My understanding is because .sub isn't a child of the a we can't reference it in css to keep the hover. 
Because the image is for only one section of the code, I can't move it to the li and reference li:hover a.
 
     
     
     
    