(new) Hungarian citizens in Hungary: health care, pensions, etc.

Hi everyone:
What benefits can new residents of Hungary who are Hungarian citizens receive? For example health insurance or pensions or any other services. Of course, as in the case of health care, we would need to buy into the system.  I am asking on behalf of older adults, ages 55+.
Thank you!

No SS benefits after a certain age unless you have at least 15 years paid into the Hungarian work system.
I am not sure what retirement age for men is here, it was 55 for women years back but now it is 60, think for men it is 62 but not sure, can work longer though if you don't have the 15 years min. in.
My husband went in to ask but he was short by 9 years, you can or at least could pay up into the system and collect but that was a few years back when we asked and really why would anyone want to pay into a system in back payments for 9 or more years only to collect the min. amount given in SS payments. Would have to figure out if you would be still alive long enough to break even.
Health care is the same if you have not paid into the system over the years you will have to pay out of pocket even in your "old age".
It is also case by case because they had called some police and others back to work in the past if they were still considered,"young" enough but had the years in to retire.
Back in the late 70's in the old times my FIL was asked to come back from retirement and given a large bonus for doing so. He had been a heavy equipment operator in construction.
Not sure if they are still asking people to come back or not, I read many construction jobs are finding it hard to find qualified people in Hungary. They are leaving for more money in the west.

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