No, they aren't "forced out of the state", and you don't need "a huge pension". Maybe staying in a high rent location like, oh, say, San Francisco or Santa Barbara, might be problematic. If for some bizarre reason you didn't buy a house years ago. But living in (say) Marysville or Susanville shouldn't be a problem. The state of California does NOT tax soc security payments, unlike many other states, so lower income people (relying on soc sec, for example) shouldn't be priced out (of anywhere except the highest rent places in the state). So you might be "forced out" of your *city* (if high rent), but not the state.
And seriously, if you didn't buy your home years ago, you should just ... well, no, I won't finish that. There are SO MANY reasons to buy, *not* doing so is just stupid. And just about anybody can buy - if you can afford rent, you can buy - you just have to put up with roommates (oh, surprise, just like if you rent!). I was famous for going on and on and on to the young hires at work about how important it was to buy *if they thought they would be living in the area for more than 2 years*.
You can't pay for the mortgage yourself? That's why you find other youngsters to whom you rent out rooms in the house you bought. People you work with, people you think you can live with. Let *them* pay the mortgage for *you*.
****, I cycled through several houses. After the first two, I didn't even sell them to "trade up" - I just rented them out after a couple of years of living there, and bought a new place. I sold off the last one about 2 years ago (and I even bought a house in 2012 because the prices were so low, taking out a mortgage on my then-paid-off-house to cover the buy-in).