When you delete an invoice, it will be removed from your business' account. At that same time, the amount owed to you by the customer would be voided. Therefore if a customer had already remitted payment towards this invoice (either partial or full), that payment would now remain on their account as an overpayment or be automatically applied to any additional outstanding invoices.
At this time, you cannot recover an invoice after it has been deleted. If you delete an invoice in error, you would need to recreate that invoice to the customer in question.