How can I output a text string when my dynamically built form is empty?
I don't know what's the code before/after and exact context in which you are using it., but this could work for you:

if(empty($options)) {
  $form['empty']['#markup'] = t('None');
}
else {
  // Form defintion.
  $form['posts'] = array(
      '#type' =&gt; 'checkboxes',
      '#title' =&gt; t('Member responses to:'),
      '#options' =&gt; $options['post'],
  );
  $form['terms'] = array(
      '#type' =&gt; 'checkboxes',
      '#title' =&gt; t('Posts tagged with:'),
      '#options' =&gt; $options['term'],
  );
  $form['groups'] = array(
      '#type' =&gt; 'checkboxes',
      '#title' =&gt; t('Group posts for:'),
      '#options' =&gt; $options['group'],
  );
  $form['submit'] = array(
      '#type' =&gt; 'submit',
      '#value' =&gt; t('Remove'),
  );
}
return $form;