<div class="mainContainer">
  <div class="topBorder"></div>
  <div class="bottomBorder"></div>
</div>
body{
  background:#0f222b;
  color: white;
}

.mainContainer{
  background:#333;
  /* Set the container width and height, if you change it, you have to reload to see it take effect */
  width:20%;
  height:200px;
  margin:auto;
  margin-top:100px;
  position:relative;
}

.topBorder{
    width: 100%;
    height: 100%;
    position: absolute;
    border:2px solid #5db8ff;
    box-sizing: border-box;
    /* Currently the original clip needs to be set in the css as otherwise the function does not work in jquery. However, this will not work well with responsiveness if you try to set distinct values at the start.*/
    clip: rect(0px,0px,0px,0px);
}

.bottomBorder{
    width: 100%;
    height: 100%;
    position: absolute;
    border:2px solid #5db8ff;
    box-sizing: border-box;
    clip: rect(0px,0px,0px,0px);
}

var topBorderWidth = $('.topBorder').outerWidth();
var topBorderHeight = $('.topBorder').outerHeight();

/* Plugin from Joshua Poehls and originally Jim Palmer, to give support clip in jquery .animate function */

/*
* jquery.animate.clip.js
*
* jQuery css clip animation support -- Joshua Poehls
* version 0.1.4

* forked from Jim Palmer's plugin http://www.overset.com/2008/08/07/jquery-css-clip-animation-plugin/
* idea spawned from jquery.color.js by John Resig
* Released under the MIT license.
*/
(function (jQuery) {

    function getStyle(elem, name) {
        return (elem.currentStyle && elem.currentStyle[name]) || elem.style[name];
    }

    function getClip(elem) {
        var cssClip = jQuery(elem).css('clip') || '';

        if (!cssClip) {
            // Try to get the clip rect another way for IE8.
            // This is a workaround for jQuery's css('clip') returning undefined
            // when the clip is defined in an external stylesheet in IE8. -JPOEHLS
            var pieces = {
                top: getStyle(elem, 'clipTop'),
                right: getStyle(elem, 'clipRight'),
                bottom: getStyle(elem, 'clipBottom'),
                left: getStyle(elem, 'clipLeft')
            };

            if (pieces.top && pieces.right && pieces.bottom && pieces.left) {
                cssClip = 'rect(' + pieces.top + ' ' + pieces.right + ' ' + pieces.bottom + ' ' + pieces.left + ')';
            }
        }

        // Strip commas and return.
        return cssClip.replace(/,/g, ' ');
    }

    jQuery.fx.step.clip = function (fx) {
        if (fx.pos === 0) {
            var cRE = /rect\(([0-9\.]{1,})(px|em)[,]?\s+([0-9\.]{1,})(px|em)[,]?\s+([0-9\.]{1,})(px|em)[,]?\s+([0-9\.]{1,})(px|em)\)/;

            fx.start = cRE.exec(getClip(fx.elem));
            if (typeof fx.end === 'string') {
                fx.end = cRE.exec(fx.end.replace(/,/g, ' '));
            }
        }
        if (fx.start && fx.end) {
            var sarr = new Array(), earr = new Array(), spos = fx.start.length, epos = fx.end.length,
                emOffset = fx.start[ss + 1] == 'em' ? (parseInt($(fx.elem).css('fontSize')) * 1.333 * parseInt(fx.start[ss])) : 1;
            for (var ss = 1; ss < spos; ss += 2) { sarr.push(parseInt(emOffset * fx.start[ss])); }
            for (var es = 1; es < epos; es += 2) { earr.push(parseInt(emOffset * fx.end[es])); }
            fx.elem.style.clip = 'rect(' +
                parseInt((fx.pos * (earr[0] - sarr[0])) + sarr[0]) + 'px ' +
                parseInt((fx.pos * (earr[1] - sarr[1])) + sarr[1]) + 'px ' +
                parseInt((fx.pos * (earr[2] - sarr[2])) + sarr[2]) + 'px ' +
                parseInt((fx.pos * (earr[3] - sarr[3])) + sarr[3]) + 'px)';
        }
    }
})(jQuery);

/* Code to actually animate the borders */

var IntervalTimer = 1;
varAnmiSpeed = 1000;
setInterval(function(){
  $( window ).resize(function() {
    var topBorderWidth = $('.topBorder').outerWidth();
    var topBorderHeight = $('.topBorder').outerHeight();
  });
  $('.topBorder').animate({'clip':'rect(0px '+topBorderWidth+'px '+(topBorderHeight-topBorderHeight+2)+'px 0px)'}, varAnmiSpeed);
  $('.topBorder').animate({'clip':'rect(0px '+topBorderWidth+'px '+(topBorderHeight)+'px '+(topBorderWidth-2)+'px)'}, varAnmiSpeed);
  $('.topBorder').animate({'clip':'rect('+(topBorderHeight-2)+'px '+topBorderWidth+'px '+(topBorderHeight)+'px 0px)'}, varAnmiSpeed);
  $('.topBorder').animate({'clip':'rect(0px '+(topBorderWidth-topBorderWidth+2)+'px '+(topBorderHeight)+'px 0px)'}, varAnmiSpeed)
  
  $('.bottomBorder').animate({'clip':'rect('+(topBorderHeight-2)+'px '+topBorderWidth+'px '+(topBorderHeight)+'px 0px)'}, varAnmiSpeed);
  $('.bottomBorder').animate({'clip':'rect(0px '+(topBorderWidth-topBorderWidth+2)+'px '+(topBorderHeight)+'px 0px)'}, varAnmiSpeed)
  $('.bottomBorder').animate({'clip':'rect(0px '+topBorderWidth+'px '+(topBorderHeight-topBorderHeight+2)+'px 0px)'}, varAnmiSpeed);
  $('.bottomBorder').animate({'clip':'rect(0px '+topBorderWidth+'px '+(topBorderHeight)+'px '+(topBorderWidth-2)+'px)'}, varAnmiSpeed);
  
  IntervalTimer = varAnmiSpeed * 4;
}, IntervalTimer);
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External CSS

This Pen doesn't use any external CSS resources.

External JavaScript

  1. https://cdnjs.cloudflare.com/ajax/libs/jquery/2.1.3/jquery.min.js