Со следующими HTML
и CSS
.container {
position: relative;
border: solid 1px red;
height: 256px;
width: 256px;
overflow: auto;
}
.full-height {
position: absolute;
top: 0;
left: 0;
right: 128px;
bottom: 0;
background: blue;
}
<div class="container">
<div class="full-height">
</div>
</div>