<div class="confession" style="border:3px solid #DDD;">
</div>

setTimeout(function(){

    var div = $('.confession');
    $({alpha:1}).animate({alpha:0}, {
        duration: 1000,
        step: function(){
            div.css('border-color','rgba(0,0,0,'+this.alpha+')');
        }
    });

}, 5000);

$(".confession").animate({
   borderLeftColor: "white",
   borderTopColor: "white",
   borderRightColor: "white",
   borderBottomColor: "white",
}, 3000);

<div class="confession" style="margin:3px;position:relative">
    text
    <div class="fakeBorder"></div>
</div>

.fakeBorder
{
    position:absolute;
    height:100%;
    width:100%;
    left:0px;
    top:0px;
    border:3px solid #DDD;
    margin:-3px;
}

$(".confession").delay(5000).animate({borderWidth: "0"}, 500);

function shrinkBorder(){
    var e = $(".confession");
    var eBorderWidth = e.css("border-width");
    if(eBorderWidth != "0px"){
        e.css("border-width",(eBorderWidth.split("px")[0]-1));
        setTimeout(shrinkBorder, 50);
    }
}

setTimeout(shrinkBorder, 5000);