With the color of that stalk/stem being all brown, I wonder if it's still alive and viable. If you squeeze that stem area is it still firm? You could try cutting that particular stem off and if it's still alive pot it up to see if it produces roots for an additional plant.
I have a couple of small Peace Lily plants and one large variegated plant. I just went out and took a photo of the base of my large plant and you can see one stalk that has a few roots visible just at the soil line. I've never noticed brown stems/stalks before.
