  The inverse eigenvalue problem of a graph $G$ is the problem of
characterizing all lists of eigenvalues of real symmetric matrices whose
off-diagonal pattern is prescribed by the adjacencies of $G$. The strong
spectral property is a powerful tool in this problem, which identifies matrices
whose entries can be perturbed while controlling the pattern and preserving the
eigenvalues. The Matrix Liberation Lemma introduced by Barrett et al.~in 2020
advances the notion to a more general setting. In this paper we revisit the
Matrix Liberation Lemma and prove an equivalent statement, that reduces some of
the technical difficulties in applying the result.
  We test our method on matrices of the form $M=A \oplus B$ and show how this
new approach supplements the results that can be obtained from the strong
spectral property only. While extending this notion to the direct sums of
graphs, we discover a surprising connection with the zero forcing game on
Cartesian products of graphs.
  Throughout the paper we apply our results to resolve a selection of open
cases for the inverse eigenvalue problem of a graph on six vertices.
