Get a WordPress registered widget instance settings.

wp-get-widget-instance.php

<?php
function get_widget_instance( $widget_id ) {
	global $wp_registered_widgets;

	if ( empty( $wp_registered_widgets[$widget_id]['callback'] ) )
		return array();

	/** @var WP_Widget $widget */
	$widget = $wp_registered_widgets[$widget_id]['callback'][0];

	$settings = $widget->get_settings();

	return ! empty( $settings[$widget->number] ) ? $settings[$widget->number] : array();
}