Edit in JSFiddle

<div>
    <ul class="nav nav-tabs">
        <li class="active"><a href="#the-tab" data-toggle="tab">Tab</a></li>
    </ul>

    <div class="tab-content">
        <div id="the-tab" class="tab-pane active">
            <div class="btn-group">                 
                <a class="btn dropdown-toggle" data-toggle="dropdown" href="#">
                    <span>Actions</span>
                    <span class="caret"></span>
                </a>
                <ul class="dropdown-menu">
                    <li><a href="#">Item 1</a></li>
                    <li><a href="#">Item 2</a></li>
                </ul>
            </div>
            <p>Menu will be cropped off under this line.</p>
        </div>
    </div>
</div>

.tab-content{
    overflow:visible;
}