The aim of an identification result for a linearly constrained problem is to show that if the sequence generated by an optimization algorithm converges to a stationary point, then there is a nontrivial face \(F\) of the feasible set such that after a finite number of iterations, the iterates enter and remain in the face \(F\). The authors generalize earlier results obtained for nondegenerate cases and develop the identification properties of linearly constrained optimization algorithms without any nondegeneracy or linear independence assumption. The main result shows that the projected gradient converges to zero if and only if the iterates enter and remain the face exposed by the negative gradient.