position: absolute;
If you apply position: absolute; to any block element(ex: div class="inner" ), the container block( ex: div class="outer" ) can't determine the dimensions of that element.
overflow: hidden;
Applying overflow: hidden; to any element means, it detect the real dimensions of that element. If that element have given dimensions( width: 200px; height: 200px; ) Overflow: hidden; determine the dimensions of the element as 200px,200px. If the element dose not specify the dimensions, Overflow: hidden determine the area of total ingredients as the dimensions of that element.
So in your case, You would apply a fixed width and a fixed height to your outer block. Otherwise you can't apply both overflow hidden, and position absolute to outter block in the same time.
If it is not possible to applying fixed width and height, css hs small tricks depending on the design. If you might explain the design more, I may explain more.