Due to Proposition 13 approved by the voters in the 70s, the property valuations are based on recent property sales. LA County can not arbitrarily raise property taxes on residences. The tax rate is based on 1.0% of the sale price of the home, and the taxes can rise by 1.1% a year, however the dirt ball politicians found away around the tax formula by adding in special assessment districts There needs to be another Proposition to make special assessment districts required to be voted on.

I don't know if the County removes the value of burned down homes from the total valuation or they just assume the house will be rebuilt at the same value and leave the valuation alone.