Around here the endless new levies have nothing to do with enforcing the claim. They're all for various social programs. I think the latest one was to fund free dance classes and other art projects.
Source: used to rent, now own
You can sue the county to get your fair assessed value lower, in order to lower your property taxes. The HOA of a condo I once owned had to do this, because values plummeted, and the county just insisted values kept going up and we owed them more and more tax.
I know a guy who somehow pays 0 property tax on a $500k USD house (don't ask me how he finagled that, but he comes from a rich family, married into a richer family and is quite shysty).
There's also more esoteric techniques like getting some parcels rezoned as farmland (which carries little to no tax burden).
But to your point (and another commenter's), there's a variety of ways a government can assume ownership of your land, even if you own everything free and clear of any debts or owed taxes. (See: Imminent Domain) In this world, you only really own something if you have the might to defend that ownership.