I don't know if it's common practice, probably not, for guest lodgings to have liability insurance coverage. Even if they do, collecting on a claim would be challenging. The claim would probably have to exceed a certain amount, a form of self-insuring to pay small, provable claims. In the current economic environment I would think the possibility that a claim for reimbursement either for treatment of an injury received on the property is next to nil, let alone reimbursement for lost work time back in the home country. The responsibility for that kind of insurance coverage should fall to the individual in the form of a temporary disability policy if they are injured at their own home or on vacation. At home base in the US, we don't even hire any workers unless they are bonded and insured.
We had a pier with a swimming platform. We let locals and kids use it at will. But leave it to a foreign visitor to think in terms of being compensated because he/she stubbed his/her toe on a nail walking out to take a swim. However, we did carry a separate liability policy because we know there's that one chance that someone would come after us for damages should they be injured because of anything on our property due to someone's lack of due caution. And that was a dozen years ago, before the wave of outsiders coming to Belize broke over.