It is well accepted that the outer core is made out of liquid iron and nickel, and as everything else it should tend to reach chemical equilibrium with its surrounding.
In particular, I would expect it to interact with the lower mantle through mixing and chemical reactions with the oxygen, silicates and other compounds. These interaction would result in the outer core slowly dissolving away into the mantle.
I would also expect this to happen in spite of the density gradient, that anyway should be less relevant down there, where the acceleration of gravity is much smaller than in the surface.
Why this dissolution doesn't happen? Why is the outer core stable?
As a bonus question inspired by this one: would any other blob of molten iron be stable anywhere in the mantle?