CSS - How to force elements to 100% of remaining/available space of parent element without extending beyond it?

You can use absolute positioning.

#b {
    width: 40em;
    height: 20em;
    position:relative;
    background: red;
}
#c {
    position: absolute;
    top: 1em;
    bottom: 1em;
    left: 1em;
    right: 1em;
    background: blue;
}

<div id="b">
    <div id="c">
    </div>
</div>