In 2018 Claeys, Kuijlaars, Liechty, and D. Wang showed that the eigenvalues of Gaussian perturbations of large Hermitian random matrices can have a macroscopic limit distribution with cusp singularities. We offer a ”free probability” explanation to their result and further show that the same ”singularity propagation” behavior also happens for Wishart perturbations. This is based on a joint work with Hari Bercovici and Ping Zhong.