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The owners of real property (land, homes, and other buildings) are sometimes, though certainly not always, liable for injuries caused to people who are lawfully present on their property.
In general, landowners must ensure that their property is reasonably safe for people who one might reasonably expect to be on the land.
This duty is strongest with landowners that invite the public to their property, such as stores, shopping malls, etc. These establishments have a very strict duty to make their premises as safe as possible Of course, they aren't expected to be insurers of their visitors' safety, but they are obliged to quickly deal with any condition which could be hazardous.
For example, if some type of liquid is spilled in the aisle of a grocery store, they are obligated to clean it up as soon as possible. It's obvious that this creates the risk that a person might slip and fall, resulting in injury. If the store fails to correct this condition in a reasonable period of time (generally, immediately when they become aware of it, or should have been aware of it), they are responsible for any injuries caused by the unsafe condition.
Homeowners, or owners of other land not open to the public, typically don't have the general duty of care that owners of publicly-accessible businesses have. They usually only have a duty to people who they have invited onto their property. Trespassers are usually not owed any care when on someone else's property (or, the duty of care is minimal).
Landlords are responsible for the structural soundness of their apartment buildings, and they have to ensure that common areas (hallways, lobbies, etc.) are reasonably safe; but any hazards in an individual apartment, which are caused by a tenant, are the tenant's responsibility. Tenants can usually not sue landlords for injuries they sustain as a result of a condition in their apartment which they caused. In fact, they can sometimes be held liable if a person they invited into their apartment is injured by such a hazard.