Property tax works against poor people being able to own property or keep property they own.
This is why elderly people who may own their homes free and clear can still be forced out of them when they retire or become disabled.
For an example tax of 2%, the property could sustain the liens for decades, allowing the owner to keep control of the land, even if they're unable to pay the taxes owed. The revenue to the government could be provided by bonds backed by those liens. Maybe require some portion of the tax to be paid in cash, and some penalty rate on the liens, to encourage payment of taxes by those that can afford them?
Are you really poor if you own valuable assets?
Aside from that, someone who owns valuable fixed property free and clear should be able to find a lender who can open a small mortgage against the property to cover taxes.
If you became poor, then maybe you should sell the property to gain more liquidity, balance your portfolio, and transfer the property to someone with enough income to fully maintain it.