FYI, foreclosure doesn't stop the property taxes, just means it gets paid by the bank instead.
In California, homes are reassessed upon sale, or if the homeowner requests a reassessment based on a drop in home value. I often review City and County budgets as part of my job, and starting in 2009 there were enormous drops in property tax revenue due to both of those things occurring. It all goes back to Prop 13--which screwed over State and local finances long-term, and on many different levels.
THis is how it works in CA: If a home increases in value, property taxes are not reassessed--the tax amount itself can go up, but only by 2% per year (that's not 2% of the home's value, but 2% of the property tax amount, which would have been only 1% when it was last assessed). So a $400,000 dollar home would have been assessed at $4,000 property tax upon sale, which is known as the "base year", an amount which would only go up 2% each year, so year 2 the owner might pay $4,080, year 3 $4,162, year 4 $4,245, and so on. However, during the same period, the value of the home might go up by tens of thousands of dollars, or even more. This is what was happening up until 2008.Property values were skyrocketing, and although the state and local governments were getting their share as defined by Prop 13, they weren't getting what they would have been getting if the property tax were reassessed upon an increase in home value.
It's 2009. In many places in CA (primarily the Central Valley) that same home might be worth half that: $200,000--and this is no exageration. In many cities it's even more drastic, like from $460k to $180k. Since Prop 13 requires the reassessment of a home if it declines in value (but not if it increases in value) the homeowner now pays $2,000. That's an immediate decrease of ($2,245) from the taxrolls. Thus, while property tax increases can only happen slowly, and over a long period of time, drastic property tax decreases can occur within a single year, severly affecting statewide and local finances. This is the primary reason why the CA State and local government is in the situation it is in. There are other problems, of course, but that's the jist of it.