Absolutely print script in footer

Cannot be overwritten

Cannot be removed/filtered

This will be done by a plugin.

These are mutually exclusive. Such a thing can’t be done by a plugin or by any other code from within WordPress. You would need to hook code in elsewhere, at the webserver or PHP level.

You could use the PHP.INI directives of auto_append_file or auto_prepend_file to force some other PHP code to always be included in a way that the user could not change. In theory, this could be used to put code into the footer, but it wouldn’t be guaranteed to work with any particular theme, because it would happen outside the WordPress context.