As you have undoubtedly read, AC has very weak fincancial capabilities at present, though I think over the next few months, beginning with Version 4, it is to be improved substantially.
Currently, the only way I know to do anything close to what you just described is to use the financial administration option and pull a report. If you have input (by hand of course) on the invoices the payments as they came in, including the write-off, then the report can show all encounters and the balance due. Balance dues > 0 are the ones you are looking for.
