Wait, their pensions depend on the health of all the companies they once worked for, rather than some independent insurance company? That sounds like a really unreliable way of handling things.
To a large extent, yes. Companies are required to pay for insurance on the pension, which is run by the federal government's Pension Benefit Guaranty Corporation [1], so it's not 100% dependent on the long-term health of the company. But the insurance doesn't necessarily cover the full pension, especially if it was a fairly generous one (there's an absolute cap of $60k/yr, and various other caps relating to years of work). In practice it does mean that how people fare in retirement depends in part on how lucky they were picking an company. If you're a retired electrical engineer who worked for IBM or AT&T, your pension is still fine. If you did the same job for U.S. Steel, less so.
That was the dream a long time ago, mainly in the 1950s-1970s. You'd work hard in school and hope for a good job at a good company like IBM or Ford, then you'd be the best company man possible to cling to that job and rise as high in the ranks as possible, then retire with a substantial % of your salary paid out in pension and generous benefits until you died.
It was real, but mostly only for the high born, the nepotistic, people in the "correct" church, and the backstabby. And of course white males only, hahah that almost goes without saying. It wasn't quite as amazing as people thought, but those who benefited sure did enjoy it.