The file EIGENVALUE contains all Kohn-Sham-eigenvalues for all k-points, at the end of the simulation. For dynamic simulation (IBRION=0) the eigenvalues might be predicted for the next step: i.e. it is compatible with CONTCAR. For static calculations and relaxations (IBRION=-1,1,2) the eigenvalues are the solution of KS-equations for the last step.
Mind: For dynamic simulations (IBRION=0) the EIGENVAL file contains some predicted wavefunctions compatible with CONTCAR. If you want to use the eigenvalues copy CONTCAR to POSCAR and make another static (ISTART=1; NSW=0) continuation run with ICHARG=1. For reasons of safety do the same for relaxation runs (IBRION=1,2).