Hi, I am curious. when a hurricane hits and buries Caye Caulker in the big wave, where do people go to be safe? Do all the buildings get washed away? If not, how do you keep your stuff safe?

They come every forty years. Last one in 2000. About a third of the houses were damaged badly some gone.
Before it was Hattie in 61 and another in about 1922.
Your stuff gets wet. There was never a big wave. The reef stops that. The water going out that was driven ashore rises in about twenty minutes and cover most of the island a few feet to head high as it goes OUT. That causes the most damage.
Smart folks build on posts. Gringoes like to build on the ground along with the young and dumb.
Many gringoes prefer to have little of value besides electronics to avoid theft and water damage at any time not just in storms.

You have a lot of warnings in most cases, a week or so. Take your family inland for a trip.
The last hurricane we didn't get enough warning and many people rushed the boats at the last minute.
Lucky we had Fermin as the Council Pres. He brought the cops out and forced everyone to go home.
By then the seas were scary and the last folks out thought they might drown enroute.

Damage after a hurricane.