Always make sure you have received your payment before accepting the order, unless you allow your customers to pay later or offer payments on invoice.
For most payment providers there is an automatic order status update. After the order, the order status is Order received. After the payment this is automatically updated to Payment received.
Usually you will also receive an email from the payment provider that the payment has been received and you can also check this in their back office.
Receiving an order does not imply that you will receive a payment!
Unfortunately, there will always be customers who try to order without paying. You should contact your customer to determine what went wrong.