Many people decide to pay for their own private healthcare without having any insurance, funding it from savings or loans. The risk of going the self pay route is that if medical costs are incurred before a sizeable fund has been built up or if heavy charges unexpectedly occur, the expense is not budgeted for.
An insurance policy which shares the costs. Some are "Stop Loss" ie the customer pays all the bills, but there is an annual limit on it, above which limit the insurer pays all the costs. Others are "Shared" where the customer pays anything between 30% and 70% of the costs, the insurer pays the rest.