not paying taxes on your property is different from not owning something and missing a recurring payment.
If you fail to pay your lease then they will reclaim that particular item.
At least in the states they absolutely do. It starts off as a tax lien which is then sold to whoever wants to buy it, so that the private sector handles actually reclaiming the land and re-listing it on the stock market.
https://www.bristol.gov.uk/council-tax/what-happens-if-you-d...
In the UK the process is different, which just shows that they don't have to take your house to reclaim outstanding taxes.
The point is that the government has options, if the property recovery value doesn't cover the missing taxes then I'm sure they will recover through other avenues. If you lease a car and don't pay, they can really only reclaim the car.
The government can take whatever they want in repayment as they are the government.