Owner of a furnished rental? You should know that the rules regarding furnished rentals are not the same as for bare boat rentals. You must therefore seriously consider the issue, because if something happens with your tenants, you may well find yourself in trouble. In fact, the tenant in question does not need to make sure of anything with regard to your property. You might as well take care of things yourself.
The insurances that I advise you to take
As far as your furnished rental is concerned, I think you should take out insurance that covers both the property in question, but also its contents that will be made available to the tenant. You also need to think about your responsibilities to your tenant, which you should insure at the same time.
Considering an insurance policy on behalf of the tenant with a waiver of recourse is also an alternative that I advise you to consider with the utmost care. You never know what it might do for you.
Finally, I also recommend that you take out unpaid rent insurance, because yes, these are quite common. By taking out such an insurance policy, you will ensure that you will not be left with nothing if your tenant does not pay the rent.
Remind your tenant that he or she is still responsible
Although in the case of a furnished rental, there is no legal recourse to force the tenant to purchase insurance, I think you should still remind them that they are fully responsible for everything that happens in the furnished rental during their stay.
Also, it would be a good idea to think about rental risk coverage. This will prevent the tenant from having to pay compensation out of pocket. As a landlord, you will also feel more secure knowing that if something goes wrong, you are well assured that you have the means to make the appropriate repairs.