I created a jsFiddle which shows the chosen-select control being \'truncated\' by it\'s parent div. And even though the overflow is se
Added border to show you the definition of your other box is staying fixed.
div.content {
position:absolute;
}

When you select position:absolute, you are effectively telling it to ignore the constraints of your fixed parent div and be able to bound outside the box.
Does this answer the question? I can elaborate further if you'd like.
absolute positioning will remove it from the flow of the rest of the document and treat it as if it didn't exist (it displays where you tell it to, but will not modify other element flow).
Try just adding a spacer like so:
CSS:
div.filler {
height:30px;
}
HTML:
...