Nonlinear phase diagram

[Axioms]

I don't understand what is going on in this graph. At the point e' there is a liquid phase outside the solidus line. The explination is that the diffusivity of the alpha phase is slower in non linear equilibrium phase diagrams. Point f'does not have the same liquid phase outside the solidus line.

 

I guess my question is how do you determine when there will be no more liquid phase under the solidus line in a nonlinear phase diagram?