Well, or new residential assessed at new rates. I'm not sure how free cities are to change their tax rates, my understanding is the major problem with Prop 13 is that existing owner's taxes can't go up very fast. But if a new resident displaces an older one, the tax value resets and the tax receipts go up. Same for building new residential, you get a bunch of taxpayers at the 'current' rate.

But I'm guessing there are also limits on overall rates because otherwise property tax rates would have gone up to make up for the 'lost' revenue from owners who are grandfathered in.