In San Pedro, and i'm sure it's the same for Caye Caulker, we have been offered lobster at Mathieu's Delicatessen a couple of times in closed season. When I remarked "isn't it still closed season?", and told the seller I wasn't interested, he backed out the door pretty damn quick. When we were living on Caye Caulker I took a fishing trip with friends of friends (just accompanying on a working fishing boat), and they pulled up a sackful of lobster, there must have been at least 80 or 90. That was 3 weeks before open.
Trying to have a tactful conversation about this with the fishermen, they said simply "if we wait til open, there'll be no lobster left, everyone's doing it so we can have a stockpile to sell on day one"... that was 3 weeks before open, go figure how long they'd been doing it and how may others had. Makes mockery of "closed" season.