The answers to these question depend on the jurisdiction. Also, not to be confused are situations where the carrier cancelled and the passenger cancelled (even if for good reason).
For tickets covered either by EC 261/2004 (EU carrier or any carrier departing the EU) or US DOT rule (any US carrier ticket anywhere or any carrier to or from the US), the passenger is entitled to a full refund to the original form of payment, that refund to be initiated within 7 days (14 if a third-party such as a travel agent).
The key to successful chargeback is to do everything in writing and to document the chargeback fully. It ought to include: 1. Copy of e-ticket receipt. 2. Cancellation notice (or something showing flight cancelled) 3. Request by passenger for refund. 4. Any response from the carrier or a note from passenger that no response has been received and no refund initiated.
Finally, make it clear that you do not accept a flight credit or other form of voucher.
In the case of a ticket covered by US DOT rules, also file a complaint. The form is online and free. DOT does not enforce individual claims, but it does require the carrier to respond in writing with a copy to DOT. A properly documented complaint (which is forwarded to the carrier) makes it hard for the carrier to do much other than respond that it has issued or agreed to a refund.