This problem of an ever increasing older population, with a declining birth rate, is a major problem for most western countries.
This is why immigration has been actively encouraged in many Western countries, as immigrants tend to have more children than the indiginous population.
How to fund this aging population is a difficult one.
The state pension will probably be means tested, so if you already have a pension or some savings you dont get the state one. That well save some money.
People who own their own homes will be expected to sell them to pay for services if they go into a home (which already happens).
People will probably also work longer, with a fixed retirement at 65 being a thing of the past.
Older people may also be expected to pay for some of their medical treatment if they have savings.
But overall it is going to be a MAJOR problem in the "west" and we may find it difficult to continue to support an ever aging population.