A custom function to log any subscription status changes.

log_sub_changes.php

<?php

// Log Subscription status changes
 add_filter( 'woocommerce_subscription_status_updated', 'log_sub_status_changes', 10, 3 );
 function log_sub_status_changes( $subscription, $new_status, $old_status ) {
	$logger = new WC_Logger();
	$subscription_id = $subscription->get_id();
	$sub_user = $subscription->get_user_id();

	switch ( $new_status ) {
		// All available statuses are "pending", "active", "on-hold", "pending-cancel", "cancelled", and "expired"
		// Add as many 'cases' as wanted for each status change
		case 'expired':	
		$logger->add( 'sub_status_changes', 'Subscription #' . $subscription_id . ' (from user #' . $sub_user . ') expired' );
			break;
		default:
		$logger->add( 'sub_status_changes', 'Subscription #' . $subscription_id . ' (from user #' . $sub_user . ') changed its status from ' . $old_status . ' to ' . $new_status );
			break;
	}
}