Typically the assessed value is the purchase price – no guarantee, but this is typical. If value drops within the first year after you buy, you can get a permanent reduction in the assessment from the County.
Additionally, if comps in your area are much lower than what you paid, even if you bought years ago, you can request (and will usually get) a one year reduction in assessed value. You can make this request every year so long as the current market value is less than your current assessed value.
I believe that Prop 13 prevents increases in your initial assessment so long as you are the owner. I do not believe you even have to live in the property for this protection.
County tax receipts are going to follow the market down. Our schools are already in budget trouble now, what about when property tax receiepts are off 20% or 30% from current? THIS IS A MAJOR ISSUE FOR LOCAL GOVERNMENTS ACCROSS SOCAL but does not appear to be on anyone’s radar.
