I solved the issue using a fallback with PHP conditionals: in my sidebar.php
I coded like the following:
<?php if( is_active_sidebar('my_sidebar') ) { ?>
<div id="secondary" class="widget-area">
<ul class="xoxo">
<?php dynamic_sidebar('my_sidebar'); ?>
</ul>
</div><!-- #secondary .widget-area -->
<?php } else { ?>
<div id="secondary" class="widget-area">
<ul class="xoxo">
<?php // Default Widget : Archives ?>
<li id="default-widget-1" class="widget-container default-widgets">
<h3 class="widget-title"><?php _e( 'Archives', 'your-theme' ); ?></h3>
<ul>
<?php wp_get_archives( array( 'type' => 'monthly' ) ); ?>
</ul>
</li> <!-- #default-widget-1 -->
<?php // Default Widget : Pages ?>
<li id="default-widget-2" class="widget-container default-widgets">
<h3 class="widget-title"><?php _e( 'Pages', 'your-theme' ); ?></h3>
<ul>
<?php wp_list_pages('sort_column=menu_order&title_li='); ?>
</ul>
</li> <!-- #default-widget-2 -->
<?php // Default Widget : Categories ?>
<li id="default-widget-3" class="widget-container default-widgets">
<h3 class="widget-title"><?php _e( 'Categories', 'your-theme' ); ?></h3>
<ul>
<?php wp_list_categories( 'sort_column=menu_order&title_li=' ); ?>
</ul>
</li> <!-- #default-widget-3 -->
<?php // Default Widget : Meta ?>
<li id="default-widget-4" class="widget-container default-widgets">
<h3 class="widget-title"><?php _e( 'Meta', 'your-theme' ); ?></h3>
<ul>
<?php wp_register(); ?>
<li><?php wp_loginout(); ?></li>
<?php wp_meta(); ?>
</ul>
</li> <!-- #default-widget-4 -->
</ul> <!-- .xoxo -->
</div><!-- #secondary .widget-area -->
<?php } //endif( is_active_sidebar ?>