I am aware that you can clear out of BVI 24 hours prior to departure, but what should you do if during this interval, something happens to delay (or cancel) your intended departure? And theoretically, let's say you cleared out at JVD and then sailed to Cooper Island with plans to sail to St Croix the next day and something changes your plans?

If there’s any significant chance you’ll overstay, just don’t clear out. Cooper is great as an overnight spot. So is the Bight if you’re looking for something on the way back.

If you haven't cleared out, you might have some trouble clearing into the USVI in St. Croix, so I wouldn't try it.

I have "overstayed" after clearing out of the BVI before and always prepared had a good reason to present to any customs officers coming on board (parts of an old impeller with tools close to the engine to show I had to replace the impeller, or having a defective anchor windlass preventing me from weighing anchor {luckily, that is just a tripped breaker away from fixing :)} That will work if you are only one night or afternoon from the 24-hour limit. I have tried to to clear out of the BVI in the afternoon and when asked about my departure plans I told them "tomorrow at noon" to give myself some leeway and they then told me to come back the next day in the morning to clear out! So now I will usually tell them "tomorrow at sunrise" to prevent my having to return to the immigration offices.

If your plans have to be changed because of motor or other thing that will affect your safety you can call immigrations and they’ll give you a extension.
They will send someone over at one point or another to confirm it.

Thanks:
I did not think of calling Immigration, I was wondering if I had to go in person, and to same location, as the paperwork would obviously not be in centralized office.