Absolutely-positioned elements are not affected by any overflow
setting if the element with that setting is not (or does not contain) its containing block (usually, this means it's not positioned).
In your case, the box is not positioned, so the text is anchored to the viewport instead of the box. The box doesn't know about the text and the viewport is large enough to contain the text, so no clipping occurs at all. You can find the gory details in section 11.1 of the spec.
Giving your box position: relative
will cause the text to be positioned relative to the box, and be clipped as a result.
#vbox {
position: relative;
width: 100px;
height: 500px;
overflow: hidden;
background: #afa;
}
#vtext {
position: absolute;
width: 100px;
top: 250px;
}
<div id="vbox">
<div id="vtext">
<p>Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget dolor. Aenean massa.</p>
<p>Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus.</p>
<p>Donec quam felis, ultricies nec, pellentesque eu, pretium quis, sem. Nulla consequat massa quis enim.</p>
<p>Donec pede justo, fringilla vel, aliquet nec, vulputate eget, arcu. In enim justo, rhoncus ut, imperdiet a, venenatis vitae, justo.</p>
<p>Nullam dictum felis eu pede mollis pretium. Integer tincidunt. Cras dapibus. Vivamus elementum semper nisi.</p>
<p>Aenean vulputate eleifend tellus. Aenean leo ligula, porttitor eu, consequat vitae, eleifend ac, enim. Aliquam lorem ante, dapibus in, viverra quis, feugiat a,</p>
</div>
</div>
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