When the SearchBox is on the right side of the screen and the dropdown width is larger than the SearchBox width, the dropdown goes outside the viewport:
Actual: https://www.screencast.com/t/4SoNcRCj
Expected/fixed: https://www.screencast.com/t/smfPgy767M

Workaround: 

<script>
    function OnClientLoad(sender, args) {
        sender._dropDown.on({ "reflowed": sender._onReflowed }, sender)
    }

    Telerik.Web.UI.RadSearchBox.prototype._onReflowed = function () {
        var that = this;
                       
        var $animationContainer = $(that._dropDown._animationContainer);

        if (that._enableScreenBoundaryDetection) {
            var availableSpace = that._dropDown._getAvailableSpace();
            var tableWidth = $(that._innerWrapElement).outerWidth();
            var dropDownWidth = $animationContainer.outerWidth();
            var overflow = dropDownWidth - (tableWidth + availableSpace.right);

            if (overflow > 0) {
                var left = parseInt($animationContainer.css("left"), 10);
                var newLeft = Math.max(left - overflow, left - (dropDownWidth - tableWidth));

                $animationContainer.css("left", newLeft);
            }
        }
    }
</script>
<telerik:RadSearchBox runat="server" ID="RadSearchBox1"
    DataTextField="ShipName" OnClientLoad="OnClientLoad" DropDownSettings-Width="500px" DataValueField="OrderID">        
</telerik:RadSearchBox>