Different laws entirely. There is nothing that would prevent the state, or community, from passing and enforcing nuisance and other laws like the ones you described, even if all confiscatory taxes were completely abolished.
There are already laws that enable tax collectors (of non-property taxes) to put a lien on your house if the tax is unpaid. Likewise, legal fines and penalties, if not paid, can result in liens, as they are treated just like any other debt. The difference with a property tax is not that non-payment of a tax, fine, or anything else could cause you to lose your property, but rather the basis upon which the property tax is levied, which makes it the most pernicious, unfair (and rightly most hated) tax of all.
The property tax is an ad valorem tax, meaning "based on value" -- a regressive tax that is not based on, nor is it concerned with, your income, ability or inability to pay. In other words, you do not have the right to own property - ("...to be secure in your...houses...") and be poor at the same time.
If you are poor and are creating a nuisance in the community, you may be without an excuse, because cleanup does not necessarily cost (like an unfunded mandate). Likewise, if you are poor, and have no income, there is no income tax. If you are poor and are not buying anything, then there is no sales tax. But if you are poor and have real property - you still have a tax bill to pay, regardless -- one that does not give a shit that you are poor. Pay up, or else you can, and WILL be evicted.
The property tax is based only on the value of what you have already paid for, or gone into debt for -- but do not, and cannot ever, completely own. All the lumber and materials used to improve your property -- included in the tax. You already paid the excise tax on those materials, but if it becomes part of the property, it now becomes subject to a property tax, as you must PAY PERPETUAL RENT TO THE GOVERNMENT FOR WHAT YOU ALREADY PAID FOR (including the taxes).
To add insult to tax injury, the property tax is not based strictly on the value of your property in most cases. There is usually a "mill rate" (or multiplier of some kind) involved, which is usually determined by government budget requirements. In other words, simplistically speaking, the government first determines what it needs, then it determines whatever else needs to be factored in as rates - in an equation such that the assessed taxable value of all property ends up being close to the amount the government budgeted for revenue.
Anyway, sorry to ramble. The bottom line is that property rights (like any other rights) are respected, inasmuch as they don't interfere with other people's rights.