You can go a lot deeper on this. Even today, about 50% of seniors would be below the poverty level without Social Security.
That's mostly okay, because the majority of seniors have the major expenses covered by guaranteed benefit pensions, Medicare and private savings, usually in the form of a house.
But things would get pretty grim without the government programs.
As far as private savings, those disappear almost immediately in the face of a medical disaster.
Things are pretty grim indeed without the government programs (Social Security and Medicare).
Bankruptcy by medical disaster should be averted by Medicare and a supplementary plan, assuming it's late enough in life. Slightly earlier, and yeah, your savings can vanish.
It's one thing to give welfare to older people who can't work to keep them off the streets and quite another to give them welfare so they can give lavish inheritances to their children.