In some (or all?) counties, if you move to another house in the same county you can keep your original tax base.

Transferring a Principal Residence Value within a County

“Proposition 60 (Revenue and Taxation Code 69.5)

Property owners of at least 55 years of age may transfer the base year value of their principal residence to a replacement principal residence. The replacement must be of equal or lesser current market value and located within the same county. Sacramento County does not allow base year transfers from other counties.”

https://assessor.saccounty.net/LowerMyTaxes/BaseYearValueTra...