they can and they have. prop 8 passed AFTER prop 13-
In 1978, California voters passed Proposition 8, a constitutional amendment that allows a temporary reduction in assessed value when real property suffers a decline in value. A decline in value occurs when the current market value of real property is less than the current assessed (taxable) factored base year value as of the lien date, January 1.
i have multiple family members who purchased during the hot market of the early 2000's. when the housing bubble burst and their properties went down 50% or more in value they were quick to apply with their local assessors for a prop 8 evaluation. the demand was so overwhelming in some regions that the processing time exceeded 6 months. i had family that receive several thousands in property tax refunds (approved applications were retroactive to date of submission) and thousands per year more in yearly reductions. it was 'rinse and repeat' with applications for all the years it has taken for those homes/properties to get back to their then sale price values (in one case 15 years-just got back there but now with the softening of the market it has dropped again so he will re-file again this year),