The only way I know is to associate the event with an exit button or link and use the Facebook Javascript SDK to actually log out to Facebook for you.
<a href="/Account/Logout" id="Logout">LogOut</a>
<script type="text/javascript">
$(function(){
$("#Logout").on("click", function(e){
if(confirm("This will also log you out of Facebook. Proceed?")){
FB.logout(function(response) {
});
}else{
e.PreventDefault();
}
});
});
</script>
, , Facebook. , , , , . , SDK .