OP is a new poster and there is tons of advice based on missing information. That simply confuses the situation. Rather than bombarding OP with hypotheticals and anedoctes of what might happen, OP has already cancelled and already has an answer from DL. So, the question is helping OP through this.
1. OP - Did your parents purchase the tickets from DL or from a travel agent? If from DL, it sounds as though these were non-refundable, but that if cancelled can be used within a year for other DL travel after a penalty. Is this what your parents want to do? When does the year expire?
2. Is there travel insurance? They might have purchased this as part of their tickets, it might be available through the credit card used for the purchase, it might be available as a special feature of a homeowners or other policy they happen to have or one of their employers' might have it (even for leisure travel) and they might not even know of it. If they have coverage, use this. No matter what, it is almost always better to have the cash.
3. Go back to DL and have a calm conversation and offer to obtain a letter from your father's doctor explaining that your father will be unable to travel on 11/28 and that your mother is needed for his care. That may result in at least a waiver of any penalty. But, that is up to DL.
As to travel insurance, even for the infrequent traveler, it is worth carrying something fairly comprehensive for international travel. The coverage tends to be cheap and the refunds are easy with proper documentation. Additionally, these policies, if you carefully choose, tend to also have other features, such as repatriation in medical emergencies. These may happen to older & sicker people more often than younger & healthier people, but even the young & healthy have bad accidents and the cost of a medical evacuation across the Pacific can exceed $150,000 and is not generally covered by standard health insurance.