What Happened to My Donkey Tail?!

I used to live in a beautiful old Victorian home that had a parlor. That room is where my piano sat and where I taught lessons. When my students arrived, they were to enter quietly and wait in a room named the family room, my husband called it the holding pen. At that time I was teaching 40 students every week and some of them would hang out in the “holding pen” for sometimes an hour or so before their lesson or stay after thier lesson until a parent could pick them up. The parlor was on the other side of the house from the “holding pen” and I could not see what was going on in that room while I was teaching a lesson. (I often wished I had a hidden camera!) I had this prized plant that takes forever to grow called a burro’s tail or a donkey’s tail (Sedum morganianum) and I began to notice that every Tuesday after lessons, that plant would have all the little cylindrical leaves stripped from one of the long stems of the plant and there would be a pile of them on the floor. I asked all of my students about this strange phenomenon and of course no one had a clue what was happening to my plant! Sure enough, this went on for weeks until my prized plant had no leaves left and eventually died.