I know someone who got left behind by
RCCL in Cozumel. She and her husband got separated. Once it started getting real late in the day, he assumed that she would head back to the ship, and she kept looking for him in port until it was too late.
In each port, there is an agent who specifically is there to help people when their travel plans go wrong. This agent helped my friend catch up to the ship in the next port, and get word to her husband that she was okay.
It was very, very expensive though. The only way she could catch up was to charter a plane. It ended up costing them about $2,500.
Travel insurance would not cover this since it was her fault.