Welcome to cruisereviews.com. While I have no information about the cruise you reference, I do have some tips about how to prepare for this rare possibility.
First, make sure you have a photocopy of your passport. A color photocopy is best. While it does not serve the same purpose, it can help with a replacement, should that become necessary. Also have an original form of photo ID (which you would have anyway in order to return to the ship) to prove your identity.
Also important is knowing who to contact. In this case, it would be the Port Agent for the specific port of call. It's easy to find this information -- it's printed in the daily activity sheet and/or port information sheet you should receive on the ship. If you don't have one, go to the ship's information desk.
Also have an ATM card (in case local currency is needed) and a credit card, as you will definitely incur some costs.
Finally, if you have travel insurance, have that information available to you, as well. Some companies give you a wallet-sized tear-off sheet with your policy number and a contact number. While insurance will probably not cover you if you are late due to your own doing (such as falling asleep on a beach, for example), you may be covered for other situations. If that's the case, keep all receipts.
This is not very likely to happen to you, but it always pays to be prepared.