I know there is probably no direct cannon to support any hypotheses made, but I have been mulling the question over in my head for some time and cannot come up with a fully satisfactory answer.
The books say that the Resurrection Stone allows one to see and converse with those who have 'passed on'. It therefore implies that it is the soul of the departed that is being communicated with but as we all (hopefully) know, Voldemort split his soul into a total of eight pieces, so what would happen if someone somehow found the Stone in the forest where Harry dropped it and decided to have a little chit-chat with The Dark Lord?
In Harry's out-of-body/in-head experience he saw the small baby-thing and Dumbledore told him that it was Voldemort's mangled soul.
so would our random discoverer see a curled up mangled-soul figure? Would they see eight such creatures? Would they see one whole and complete Voldemort as all the pieces of his soul somehow combine again once all are re-united in the 'afterlife? Or do people have other theories on how the Stone allows conversations with the dead?