I live in Grand Cayman and am a cave diver. I've visited the caves, and specifically asked if there were any that were flooded and suitable for diving. I was told no, the only ones that had water had it just a few feet deep, and didn't go anywhere. That said, the property owners had 3 caves open for tours, but claimed there were over 150 on the property.
In the time I've lived here, I've heard rumors and urban legend about a cave system that goes deep below the island. No one seems to have any more insight. It stands to reason there are some flooded caves here. The geography is similar to other islands with caves, we have the dry caves, and local construction diggers I've spoken to claim they hit flooded pockets when drilling regularly.
On my down time I've investigated a few potential leads. The biggest so far is a very tight entrance that leads in perhaps 100 feet, and winds down to 80 or so. We found cave line inside, that leads even deeper, but goes through a no-mount passage I'm not willing to push through.