Zillow's estimates are definitely questionable and I don't want to be seen as defending their precision. However, unless you're referring to an actual house addition or something like earthquake retrofitting, most capital improvements are rounding errors to the value of a house in California. Land alone (vs. "improvements") for a house purchased recently is ~70% of the value and you can see this broken out on a property tax statement. Replacing knob and tube wiring or putting in AC is low tens of thousands of dollars at most and frequently those minor things aren't even reported to the assessor. Sure, an old house that hasn't been updated isn't going to sell for as much as one that has, but unless it's a major change, it isn't going to be hundreds of thousands in difference.

Because I can't query Zillow's data, I don't know any better way to do it than find a neighborhood where most of the houses are old and just see what their property taxes are one by one. In my neighborhood which was built in the 1910s and 1920s, there's quite a few examples of people paying sub $1k in property taxes per year. It isn't a majority or anywhere close to it but within a couple blocks of my house I found nearly 10 examples. I even found a 4-unit multifamily paying just under $1k total.

If you want a pure anecdote, a friend in a nearby house just had the knob and tube in their house replaced with modern electrical (~$35k). The electrician found gas lines in the 1st floor ceiling for indoor gas lighting. Although the lighting fixtures were gone, the gas lines were still hooked up to the main house gas line.