var element = document.getElementById('div');

element.addEventListener('DOMSubtreeModified', myFunction);

function myFunction(e) {
    console.log(element.innerHTML);
}

setTimeout(function(){
    element.innerHTML = 'Hello World!';
}, 1000);

setTimeout(function(){
    element.innerHTML = 'Hello Space!';
}, 2000);

참조

https://www.phpschool.com/gnuboard4/bbs/board.php?bo_table=qna_html&wr_id=281733