What seems odd to me (if I understand it correctly) is that prop 13 keeps your property tax low, but you still get the full benefit of the appreciation in price when you sell the property. It kind of seems like if it's artificially keeping the tax low, the full tax bill should come due at some point, which would logically be at the change of ownership.
Property tax is the recurring value tax, kind of a wealth tax while you hold a property, and prop 13 does shield much of the appreciated value from this. A new homeowner might be paying 1-2% of market price per year, while an elderly neighbor might pay 1-2% of an assessed value that is closer to a market value from 20+ years ago. The assessment does increase at a very slow rate, and in larger jumps with remodeling or other improvements.
At the sale, the appreciation becomes realized as capital gains income. There are some rules making a portion of gains tax-exempt for a typical homeowner, but the remainder of a large appreciation is taxed as income. There can also be a sales/transfer tax on the transaction, which is of a comparable rate to the annual property tax rate.
The third significant event is inheritance, where the house could pass to an heir without a sale and have its basis updated to current value. This is when the appreciated gains can really go untaxed.
