Sounds to me like a pencil eraser that gets hard and won't erase. If soaking in water doesn't work, I'd try coating it with rubber cement and letting that dry, or taking a sharp pen knife to it and cutting away a layer all around, because I'd figure I have nothing to lose, it already doesn't work.
And I'd probably replace it no matter if that worked or not, because I have about a dozen seam rippers all over the house, lol.