This is a strange one but looks like $dom->saveHTML() is stripping tags from inline javascript
$domStr = '
<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8"/>
<title>my page</title>
<script>
var elem = "<div>some content</div>";
</script>
</head>
<body>
<div>
MY PAGE
</div>
</body>
</html>
';
$doc = new DOMDocument();
libxml_use_internal_errors(true);//prevents tags in js from throwing errors; see php.net manual
$doc->formatOutput = true;
$doc->strictErrorChecking = false;
$doc->preserveWhiteSpace = true;
$doc->loadHTML($domStr);
echo $doc->saveHTML();
exit;
http://sandbox.onlinephpfunctions.com/code/ad59a2a1016b2128e437ef61dbe00f1c511bff8d
if you use libxml_use_internal_errors(true); you will not see what is wrong but if removed you get
<b>Warning</b>: DOMDocument::loadHTML(): Unexpected end tag : div
Same thing happens with
$doc->formatOutput = false;
Any help is appreciated.