How to change value in wp-include/taxonomy.php without exchanging the WordPress-core

There is no way to make the tag of a private post showed up by default, at least for now. I was hoping wp_tag_cloud be the answer but it isn’t. One alternative aside from hacking the core code is to create your own widget through plugin. But then I found a plugin that does exactly what I want.

https://wordpress.org/plugins/ultimate-tag-cloud-widget/screenshots/

hope that helps.