I find bark pieces under my mulberry tree that are about 1/4 x 1 1/4 inches in size. I can't see where they are coming from but they are falling a lot more than they were last year. I don't have a way to send a picture. The bark looks fresh when it falls and has the appearance of having been whittled off from one of the branches except that the edges on the sides are not slanted as they would be with a knife cut. The ends are rough. The tree is 40 years old and produces many berries. I have it cut back every other year as it is a rapid grower.
Mulberry Tree Bark Problem.
Certified GKH Gardening Expert
Mulberries are insanely fast, and vigorous. What you are experiencing is likely something that a bird or other pest is doing. These trees are rather hardy, and I do not believe it to be in any danger. the tree will give you definite signs of distress when it isn't doing well. It will likely recover, though. I see no reason to worry here.