Your society will eventually be a small number of immortal infertile old people.
Consider old people in a culture where they are supported by their families. The old people contribute but they do not work a job or bring in food. They depend on younger people in their family to do that. The same is true for children - until they grow up they too are dependent on the breadwinners. If the breadwinners in the family die or are disabled, it is the end of the family. If there are too many old people, or children they may be more than the breadwinners can support.
Your society (here in the role of family) is supported by reproductive age individuals. Because the old do not die, reproductive age persons are increasingly in the minority.
Human societies of all sorts are prone to dieback because of famine and disease. Hunter gatherers in particular and especially those confined to an area are vulnerable to food shortages - they cannot control food quantity like agriculturists can and this keeps population density low.
Your population will occasionally suffer more deaths than usual because of famine. Your old are as durable as your young and so under this sort of stress starvation is equally probable for each individual. As reproductive age persons are a smaller and smaller percentage of the population there will come a time when a dieback takes all of them.
Your population will then be composed of all old people and it will slowly shrink because of subsequent food shortages, death from accidents and so on.
There will be a time when the land available can easily supply the remaining persons and there will be minimal death from famine. Death from accidents will be very rare too as these ancients will be extremely wise and canny, and will not make mistakes. This population could go on for a very long time.