Here the background is its original size, the same size as the element it is applied to.

Here we have the same div and background, plus a "slice" inside it with the same background as the parent. The slice has a red border. Note that the backgrounds are the same size.

Here the original div has been resized and the backround has been resized using "background-size: 100% auto;".

Here the resized div has the same slice in it. Note that the slice's background is no longer the same size as the background of the parent element. What I would like to see is an option to apply backgrounds to child elements as if they were being applied to the parent. "Propagate" may not be the best term.

    parentEl {
      background-size: 100% auto propagate;

So that the end result looked like this...