JSFiddle - React, Tailwind, and code Playground

HTML

<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>

    <div>
        A long option that gets cut off
    </div>
    
    <select>
        <option>One - A long option that gets cut off</option>
        <option class="selected" selected>Two - A long option that gets cut off</option>
    </select>

CSS

select, option.selected {
   width:100px; 
    overflow:hidden; 
    white-space:nowrap; 
    text-overflow:ellipsis;
}

JavaScript

$('select').on('change',function(){
    $(this).find('option').removeClass('selected');
    $(this).find('option:selected').addClass('selected');
});