Sure looks like a peace lily to me, although it looks to be suffering quite a bit. No judgement btw...my office peace lily often looked a bit like this before I brought it home; the problem was inconsistent watering i.e. too dry. Unglazed terracotta pots like that one dry out much more quickly than ceramic or plastic, so yours may have been underwatered. Peace lily is a thirsty plant.
What came out was a division of the plant. It seems to have lost its lower roots but I see new root nubbins beginning to form on the piece of the stem that's left. I would not cut off anything from the bottom. If you want to propagate it, then it's definitely worth a shot. I would personally stick this right into a pot with a drainage hole and a good well-draining potting mix but it will probably grow in water, too.