If you're using IPN, PayPal sends an IPN post when a subscription is created, a payment is made, and when it expires. You can use that IPN post to trigger a script to send your buyers an e-mail. That e-mail can include a link to your site where the button is located or a link the buyers can click to be redirected to PayPal and resubscribe from there.
There isn't a guaranteed way to have buyers return to your site after their subscription expires. Sending them an e-mail with their different options and an explanation that their subscription has expired is a fair way of handling the situation.