If your customer has paid a bill late and then not paid the reminder fee and/or the interest on late payment, you can choose to write-off the remaining balance.
The invoice will then be marked as paid and completed. The receiver of the invoice will not receive a notification of the write-off, but can see it in on the invoice history timeline.
Note that you can only write off sums that exceed the principal amount. To write off a sum on an invoice, you click 'Manage' and then 'Write off'.