If possible you can change the div to an textarea and use .change().
Another solution could be use a hidden textarea and update the textarea same time as you update the div. Then use .change() on the hidden textarea.
You can also use http://www.jacklmoore.com/autosize/ to make the text area act more like a div.
<style>
.hidden{
display:none
}
</style>
<textarea class="hidden" rows="4" cols="50">
</textarea>
$("#hiddentextarea").change(function() {
alert('Textarea changed');
})
Update: It seems like textarea has to be defocused after updated, for more info: How do I set up a listener in jQuery/javascript to monitor a if a value in the textbox has changed?