You use wp_nonce_field with the fourth parameter set to false. This way you can get the nonce field instead of echoing it:
$end_data .= wp_nonce_field( "name-of-action", "name-for-the-form-field", true, false );
$end_data .= '<input type="text" class="ss_title_form_ajax_' . $this->id . '" limit="133" value="' . $this->native_title . '" size = "60" placeholder=""/>';
$end_data .= '<span class="ss_title_form_ajax_' . $this->id . '"></span>';
$end_data .= '<span id="ShowMe_' . $this->id . '">' . ( 60 - strlen( $this->native_title ) ) . '</span>';
//-------------------------
foreach ( $this->have_results as $keywords_rf ) {
$end_data .= '<span class="user_select_rf" data-role="' . $this->id . '">' . $keywords_rf . ' </span>';
}
//-------------------------
return $end_data . '</form>';
If you can not modified the code if the form class, you can use wp_nonce_field as described about and insert it on the form string with any appropiate PHP method. For example with substr_replace.