Top-tompak,
 и что не так работает?
 
<!DOCTYPE HTML>
<html>
<head>
  <title>Untitled</title>
  <meta charset="utf-8">
  <script src="http://code.jquery.com/jquery-latest.min.js"></script>
</head>
<body>
 <div class="wrap">
        <div class="question">акдбука</div>
        <div class="question">акажср</div>
        <div class="question">аксмронббложбжж</div>
    </div>
 <input type="text" name="question" placeholder="Вопрос">
<script>
$(function() {
    $('input[name=question]').keyup(function() {
        //console.log('keyup()');
        var question = $('input[name=question]').val();
        //console.log('question - ' + question);
        $('.question').each(function(k, v) {
            //console.log('value - ' + $(this).text().toString());
            var val = question + '[^а]*$';
            var re = new RegExp(val, 'i');
            if (re.test($(this).text()) && question) {
                alert('This ok - ' + $(this).text().match(re));
            };
        });
    });
});
</script>
</body>
</html>