Once a billing document has been posted, normally the responsibility moves from the sales department to the finance or the credit management department. They track the overdue payments. Within the dunning function you can send out dunning letters and post additional charges. Dunning is within FI.
To my knowledge there is no automatic transaction in SD post fees. If you would like to use billing documents to post charges to your customer, in certain countries this would be seen as a taxable event and you would need to charge the customer additional VAT.