Ownership and private property makes them liable for what happens on that private property, yet they are somehow exepmted from that liability. So all perks and none of the responsibilities.
Whether liability and damages are assigned would depend on the details, but the principle is quite clear here.
Otherwise yes, it is quite possible to be liable for whatever happens on your private property. If drug deals are taking place between third parties in your house won’t you be liable? If you allowed those parties there you most definitely will be.