When someone is injured by something dangerous on private land, the occupier is responsible. They are the person in occupation or control of the place - that is, the one who has the right to decide who to admit and who to exclude from the land or premises. The occupier may be, but is not necessarily, the owner/landlord.
Both tenants and landlords are occupiers and are responsible for injuries caused by defects in rented premises [Civil Liability Act 1936 (SA) s 19]. The responsibility of a landlord is limited to injury, damage or loss that happened because they did, or failed to do, a certain thing while carrying out an obligation to maintain or repair the premises, or where the landlord did not carry out that obligation [Civil Liability Act 1936 (SA) s 21].
All occupiers, whether tenants or landlords, should take out house and/or contents insurance which must include cover for people injured by dangers on the premises (public liability insurance). This latter insurance is less expensive and can be taken separately if required. When someone has been killed as a result of a danger on private premises, the deceased person's spouse or children may have a claim against the occupier.
In some cases, someone other than the tenant or landlord has been held by the court to be the occupier, but this is rare and depends on the facts of the case.