One option would be to use JavaScript and have a function for when the submit button is clicked, it will check the value of the signing authority radio button and if it's "Yes" then it will blank out the values entered into the fields that appeared when the option was originally "No"

In an example form, have the signing authority radio button with values "Yes" and "No". Give it the CSS class name, signingauth. Then add a second field to the form, for example, a single line field for "Name" and give it the CSS class name, name. Then configure your field rule to show the name field when signing authority is "No"

Now you can use JavaScript like the following

$(document).ready(function () {
  $('.action-btn').click(function() {
    $('.signingauth input:checked').each(function(){
      if ($(this).val().replace(/V_/g,'') == 'Yes'){
        $('.name input').val("");
      }
    });
  });
});

This way, if the user clicks "No", inputs a name, then clicks "Yes" and finally decides to click "No" again, the name that was typed in won't be lost. The JS will wait until the user clicks the Submit button and checks to see if the signing authority is "Yes" and if it is, then it will blank out the value entered into the name field before actually submitting.