While a radius (or reduced circumference) can be deemed a stable radius for matter that has collapsed to Planck density/pressure, r=0 would still apply to the outer edge of this radius as this would be the end of spacetime (though some kind of bounce would probably stop this occurring, the collapsed matter oscillating close to Planck properties), the volume of matter with Planck density/pressure contained within the radius would be without dimension, as with these properties, the energies that distinguish matter and space are supposed to combine. I'm tempted to say that the Planck matter would be supersymmetric but this would be speculating. It's also fair to say that no matter how little, spin would have some effect on the final collapse of the singularity which may go some way of stopping the matter from reaching absolute Plank properties, and as stated, high energy virtual particles would probably play some part also.
The following paper is a good overview of the different types of singularity-
http://www.unc.edu/~mgood/research/Singularity.pdf
The following papers are a bit maths heavy but insightful-
Singularities and Quantum Gravity
Authors: Martin Bojowald
http://arxiv.org/abs/gr-qc/0702144
Loop quantum gravity and black hole singularity
Authors: Leonardo Modesto
http://arxiv.org/abs/hep-th/0701239
On the black hole singularity issue in loop quantum gravity
Authors: A. DeBenedictis
http://arxiv.org/abs/0907.0826
The following isn't in a user friendly format but is also insightful-
Quantum Foam and de Sitter-like universe
Authors: P. A. Zizzi
http://arxiv.org/abs/hep-th/9808180
There's also the matter of the weak singularity at the inner horizon of rotating or charged BH's which if applies may render GR mute before even reaching the centre of the black hole.