Well, no. The singularity is not what consumes the matter, it's the event horizon. What happens at the singularity is indescribable, even if that singularity is a 1 dimensional ring caused by the momentum of the spinning body. However, this creates a region around the event horizon called the ergosphere. Matter can leave the ergosphere, however if it does it will have gained energy, which will have taken momentum away from the black hole. I think this is what you mean by popping back out, but this isn't exactly popping back out, it's more over like stealing the rotational energy from the black hole, but never actually falling in.