Index: wp-includes/widgets.php
===================================================================
--- wp-includes/widgets.php	(revision 41324)
+++ wp-includes/widgets.php	(working copy)
@@ -1036,6 +1036,10 @@
 function the_widget( $widget, $instance = array(), $args = array() ) {
 	global $wp_widget_factory;
 
+	if ( ! isset( $wp_widget_factory->widgets[ $widget ] ) ) {
+		return;
+	}
+
 	$widget_obj = $wp_widget_factory->widgets[$widget];
 	if ( ! ( $widget_obj instanceof WP_Widget ) ) {
 		return;
Index: wp-includes/widgets.php
===================================================================
--- wp-includes/widgets.php	(revision 41324)
+++ wp-includes/widgets.php	(working copy)
@@ -1036,7 +1036,11 @@
 function the_widget( $widget, $instance = array(), $args = array() ) {
 	global $wp_widget_factory;
 
-	$widget_obj = $wp_widget_factory->widgets[$widget];
+	if ( ! isset( $wp_widget_factory->widgets[ $widget ] ) ) {
+		return;
+	}
+
+	$widget_obj = $wp_widget_factory->widgets[ $widget ];
 	if ( ! ( $widget_obj instanceof WP_Widget ) ) {
 		return;
 	}