Don't know what critter is responsible, but.....
Friday I discovered that one of my trilliums had been dug up, so I simply re-planted it.
Saturday I found that the same plant had been dug up again. I re-planted and placed 3 fist-sized stones close around it.
Sunday it rained.
Today I walked around the yard .and took some photos. Viewing them on my computer I discovered that the same trillium had been dug up AGAIN and the stones moved. See circle on photo showing plant with roots.
Went back out, replanted the plant AGAIN, replaced the stones with ones 2/3 the size of my foot, and sprinkled about 1/4 cup of red pepper flakes on the area. We'll see what happens.