Let $X \in \mathbb{R}^{p\times p}$ be a large square matrix, consisting of i.i.d. Gaussian entries. Then it is known that the singular values of $X$ follow the Marchenko-Pastur law.

Now let's introduce an adversary, who arbitrarily selects $p/2$ rows of X and form a submatrix. Can the adversary succeed to make the singular values of this matrix look very different from the Marchenko-Pastur law of a $\frac{p}{2} \times p$ Gaussian matrix?