This is a misleading and extremely outlying example. No one in CA, even if they bought their house for $80,000 and never made a single capital improvement, still has only $800 property tax bill, because it goes up each year (just not as much as the market value). And to get an increase of $20K in property tax, the house would have to be worth $3,000,000, which is still far above the median.
More importantly, the income tax benefit is orders of magnitude a bigger deal. Income tax on a $2,000,000 gain would be 23.8% federal at least, and probably well over 10% California (so about $650,000). Yet they will pay none of that, due to the basis adjustment to fair market value upon death of the owner(s).
If the heirs can't figure out how to keep the house via a secured loan and their $650,000 in income tax savings, they probably have much more pressing money problems to deal with I imagine.