Wealth taxes have been discussed, but I'm not aware of anywhere they
exist, other than the specific case of a property tax.
Many European countries and most Western and Northern European countries (as well as Argentina) have wealth taxes. Many more countries globally have taxes on inheritances or estates which mutes the effect of inherited wealth on wealth inequality.
Also, many countries have social insurance taxes, typically impose on the basis in employment income, that fund universal pensions, health care and other social services, in which the distributions of benefits may be more equitable that the taxes that pay for them.
Has any country or region had a policy which relieves the poor from
paying to protect the property of the wealthy?
Obviously, an answer like this cannot be a comprehensive list all of redistributive policies ever adopted anyway, but it does identify a few of the more notable examples to give you a favor of what they look like in some places.
Many countries have at one time or another nationalized entire industries that were previously owned by wealthy elites, or to pre-empt wealthy elites from doing so in the first place.
For example, many countries have nationalized oil, gas and mineral resources of the country, and exploit those resources with a state owned company.
In the United States, Alaska taxes oil and gas production, puts that money into a government fund, and then distributes profits from that fund to every Alaskan resident annually on a per capita basis, in one of the most extreme socialist redistribution schemes in the United States.
Policy wonks from a variety of political backgrounds have sought to generalize this concept to establish a "universal basic income" that everyone gets simply for being alive paid for with tax funds.
Many oil or mineral rich monarchies or authoritarian regimes use nationalized/royalty owned oil and/or mineral wealth to dramatically limit domestic taxation and to fund a welfare state for average citizens, sometimes with straight cash dispersals, sometimes with heavily subsidized prices for certain essentials of life, and sometimes by heavily subsidizing services like health care and education.
Airlines, merchant shipping, banking, and defense contracting are other commonly nationalized industries.
Inequality Reduction Through Real Estate Market Interventions
Until quite recently, the lion's share all of the residential real estate in Singapore was government owned and rented to families rather than owned, and strong vestiges of that system still remain. As a result, the economic value of appreciation in the nation's residential real estate is nationalized. So, fortunes like those of Republican President Donald Trump, and Colorado Governor John Hickenlooper, a Democrat, both of which involved substantial wealth accumulation from real property appreciation, probably wouldn't have happened in Singapore.
New York City has a rental control system designed to prevent the wealthy from exploiting the poor (with mixed results) and many other places in the U.S. have affordable housing system that creates some stock of affordable priced, price controlled housing at the expense of developer who want to sell market priced housing.
In communists regimes, and other regimes with strong communist leanings that call themselves socialist, land reform is another common redistribution tool. For example, Zimababwe expropriated land from white landowners who acquired that land in the colonial era and prior to reform owned most of the productive land in the country. This absolute redistributed wealth, but it also had catastrophic effects on agricultural productivity because the new land owners installed by the effort often lacked the skill set and resources to exploit the land effectively.
Similar land reforms took place in many other places, including in early days of the Soviet Union and after the Communist Revolution in China, in both cases resulting in mass famines and tens of millions of deaths, until reforms stabilized those respective agricultural sectors.
Inequality Reduction In The Criminal Justice System
An example that is particularly relevant since the question alludes to the use of the criminal justice system to enforce property rights is that in Germany and some Nordic countries, they punish many less serious criminal offenses with "day-fines" rather than incarceration. The fines are codified for particular offenses and imposed based upon a number of days of the offender's income, which is then determined administratively. So, for example, the day fine for drunk driving might be 5 days of income. But, for a poor man, that fine might work out to be $400, while for a rich man, that might work out to be $5,000. Countries with day fines are notorious for having the most expensive speeding tickets in the world in cases where a day fine is imposed on someone with an extremely high income like a CEO of a major company.
Policies Reducing Inequality In The Private Sector
Some countries have policies that promote reductions in income inequality within the private sector, rather than through direct government redistribution.
For example, Germany provides strong rights for unions in medium and large sized businesses including a right for unions to have seats on the board of directors in a practice called co-determination.
The town of Mondragon in Basque, Spain has organized much of its economy on a worker owned cooperative basis. Many plywood factories in Oregon, and many parts of the agricultural industry in the United States above the individual farm level, are similarly organized on a cooperative basis.
In Japan, a system of lifetime employment in many big businesses, a tradition of employer provided benefits such as housing in many cases, and a wage system in those kinds of businesses where workers receive a substantial share of their annual income in the form of an annual bonus whose size can be used to buffer good and bad years for a company sharing risks and rewards with workers instead of limiting the risks and rewards to an investor class, have contributed to low levels of income inequality in the Japanese economy relative to comparably developed countries with comparable levels of government spending on welfare state type programs in other countries. Effectively, modern Japan (in the tradition of late 19th century Prussia) internalized much of its welfare state into big businesses, rather than implementing it at the government level.