In Japan, except for certain areas in the top major metros, only land has value. Buildings lose value over the life of a 30 year mortgage due to the changing nature of earthquake regulations for buildings. It will almost always be cheaper to tear down and build new than retrofit. Its also why Japan has very creative residential architecture- owners can build what they want without caring about resale.

Many non Japanese who are buying in Japan without understanding this fundamentally different aspect of real estate in Japan do so at their own risk.

This may depend on jurisdiction. UK buildings insurance usually covers subsidence (although it may then be difficult to sell the property, as any buyer will have difficulty getting their own insurance even after a repair)

I don't know specifically about mines or sinkholes, but I don't think they are generally excluded. However one difficulty would be that buildings are generally insured up to the value of the rebuilding cost, IE what it would take to put the building back after it was completely destroyed. But in the case of a mine or sinkhole, the land itself may also be unusable. In an expensive city the rebuild cost may be only a fraction of the cost of buying an equivalent home, including the land it sits on.