No one knows what happens that close to a singularity.

In quantum gravity theory, there are no singularities in the gravitational field. It is simply replaced by a region of spacetime where the graininess of spacetime becomes evident at the so called Planck Scale. In this theory, all fundamental particles are believed to be some kind of 'loops' of spacetime also of about the size of the Planck scale, 10^-33 centimeters, individual particles just dissolve away into the quantum froth of spacetime at these scales.

But we do not know for sure, and have absolutely NO way of finding out.

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