JSFiddle - React, Tailwind, and code Playground

HTML

<div id="page_site" style="width: 300px;"> <!-- ширина страницы сайта -->
	<div class="c_wrap" style="border: 1px solid #E6E6E6; height: 20px;">
		<div class="c_name" style="float: left;">1234567890абвгдежзик1234567890лмнопрст1234567890</div>
	</div>
</div>

JavaScript

(function(){

	var cWrap = document.querySelector('.c_wrap'),
      c_name = document.querySelector('.c_name');
      
  (function req() {
     var checkWidth = function() {
     
     	var cWrapWidth = cWrap.offsetWidth,
          c_nameWidth = c_name.offsetWidth;
					console.log(c_nameWidth);
          if (c_nameWidth > cWrapWidth) slice() && req();
     
     }();
     
     function slice() {
     	var text = c_name.innerHTML;
          text = text.substring(0,text.length-1)
     	c_name.innerHTML = text;
      
      return true;
     }
     
}());


}())