Probably the oldest form of insurance is existence is funeral insurance, which takes cares of burial (and now cremation) costs at death. In developed economies, its popularity has vanished, while it is still very common in Africa. One reason could be that when life insurance is available, people believe it is sufficient to cover funeral costs, and the beneficiaries are committed to take care of this. When life insurance is not available or when not commitment can be elicited from descendants, then funeral insurance ensure your body is properly disposed of.
Erlend Berg writes a model along those lines and finds that only middle income should favor funeral insurance. The rich do not face a tight budget constraint and the poor cannot afford it. Then using a marketing survey conducted in South Africa finds results that are consistent with the model. This lack of commitment in Africa for financial matters is pervasive. It is, for example, at the heart of the strange institution that ROSCAs are.