We don't have absolute property rights now and we never have.

Right, but they would steadily decline under basic income.

In order for the system to sustain itself, you need to tax something other than income. Otherwise, the BI scheme bankrupts itself as people drop out of the workforce due to technological unemployment and due to the allure of free money with no need to work. We can already see this happening with pensions and social security. I don't think it's hard to see why an income tax based BI would collapse under the load of freeriders.

That means that the majority of the taxes need to be coming from a combination of consumption taxes and property taxes. Since we are also discussing technological unemployment, we can assume that the cost of commodities is also going to steadily decline - which means property is the most valuable thing to tax and where most of the funding is going to come from.

Due to technological advancement making property ownership redundant and due to property taxes making property ownership uneconomic, private property would slowly phase itself out of society. Why waste time and money maintaining, paying taxes, and insuring private property when you can just rent everything you need at a fraction of the cost?

Eventually, the only ones that own anything are the ones that own the means of production and high-income hobbyists that can afford to waste money on property.

I don't really see this as a good outcome, because the massive inequality undermines democracy. After all, why should a politician listen to voters when the person that pays all the local taxes and owns the local automated factory says otherwise?