We have a term "apparently deceased" for these situations as not even a doctor could legally declare someone dead in flight. The body is put in a body bag (head out) and usually placed in their seat for the remainder of the flight.
In a previous airline, we had a very overweight pax die en-route to Florida from the UK. It was particularly traumatic for the family as it was Granddad taking two sets of family and grandkids to the holiday of a lifetime to Disneyland. We couldn't more him or relocate passengers on the full flight. However, my sympathy for the family waned a little when I head a week late that on repatriation of the body, his widow had asked if she could use her dead husband's duty free allowance. The travelling British public at their best!