Off loading the remains at a random location would likely result in significant additional expenses for the family.
Funeral homes will charge a not insignificant amount to pick up the remains from the airport and and will again bill for return delivery to the airport. They would also charge a storage fee since they are not contracted to handle the entire process. An air shipping container would have to be purchased in addition to paying the cargo charges. I wouldn't be surprised if diverting would cost the family an additional $2k or more.