According to GR no, once inside the event horizon the singularity is no longer a point in space, it is a point in time. It is unavoidable, just like “next Wednesday” is unavoidable. The matter that composed the neutron star must collapse and encounter the singularity at some point in its future.

More speculative theories offer other solutions. String Theory, for example, proposes “Fuzz Balls”, so called because the event horizon would be “fuzzy” at the smallest scales. The interior of the BH would be a degenerate matter composed of the fundamental strings, not empty space. Obviously very speculative.

We need a theory of Quantum Gravity to better understand the interior of a BH.