I don't know if this is what you mean:
Technically, when you rent a premise, the owner of the property must insure the structural dwelling and the adjoining land. Included in that policy would be public liability to cover the possibility of a person/s that may injure themselves while on that property, either invited or uninvited, and if the injury proved to be caused by the negligence of the said owner either by failure to rectify something that may be unsafe or failure to comply with law.
It is responsibility of the tenant leasing or renting, to insure their own contents, that being their own furnishings, with a contents insurance policy, whether it is a house or an apartment.
Such things as curtains, carpet, stoves, hot water system etc would also be the responsibility of the owner and not the tenant, but if proved to be the tenants fault, then the owner will sue for damages.
I don't fully know how some insurance companies cover the "Act of God" clause, which is, in this case, is the property owners problem. I do understand that lightning strikes are covered in most policies. War, terrorism, sky junk such (as satelites) and certain areas of acts of god are not covered.
So in this case, the structural loss would be imposed upon the owner/s insurance company, if the tenant was to have lost possession due to fire or damage to electrical goods due to a power surge, then that would have to be recovered from the contents insurance of the tenant. If the owner did not have insurance he is in a spot of trouble. If the building is classed as inhabitable until rectification then he is going to have to cough up a lot of money for relocation of tenants. This is usually negotiated into a policy.
Our house that we owned at Bray Park in Brisbane, had a colourbond fence, newly erected and it took a direct hit during a storm, it melted part of the kids pool and also resulted in a power surge which blew some electrical appliances. Our insurance policy covered the lost items and we had them replaced with no problem.
You must check all policies what they do and don't cover.
Sorry for the ramble but hopefully that is what you meant.
Col