In the second interpretation, long-term forward real rates are a measure of an equilibrium “norm”, rather than a reflection of a monetary-policy induced compression of term premia. Another way to look at the outer maturities along the real forward curve is to interpret these rates as a market measure of the equilibrium real rate.
That is, they reflect the markets’ view of the real cost of borrowing that can be sustained by an economy that is neither overheating nor decelerating. Indeed, barring preferred habitat and extreme price inelasticities on the side of potential sellers, at those maturities all shocks should have dissipated, and the economy should be expected to have returned to a sustainable path.