While propane-fueled refrigerators are probably not an option for apartment dwellers, they are worth looking into for someone with a stand-alone house and/or BOL. For instance, this 8-cubic-feet refrigerator
can run on either 110-volt AC electricity or propane. When using propane, it burns .275 gallons per 24 hours, so one 20-pound propane tank will fuel it for about 17 days. Since the linked refrigerator is built by Dometic, I suspect that Dometic's smaller refrigerators might use even less propane.
Meanwhile, I found this Web page
that features full-sized, propane-fueled refrigerators that can be converted to use natural gas in place of propane. Even the largest CrystalCold refrigerator from this site is rated to run for 13+ days on 20 pounds of propane....
Unfortunately, I saw no indicator on the linked site that CrystalCold refrigerators were fitted for 2-way (propane and electric) operation.