Probably the best way would be to have a new type of payment called "Write off debt". This would bring that person's balance to zero, but would also record the fact that they never paid. We could also use those records to ensure that people can't book again. And we'd also have an explicit record of money "lost" in this way.
If the person does want to book again, they would have to have a conversation with you. In that case we could settle the account a different way - we'd agree to waive an earlier fee (i.e. choose custom discount, reduce the "amount due" to zero), and then delete the "write off debt" record, which would allow them to book again.
From my email: