When leather gets wet (asuming they were all tanned) it streaches. When it drys out again it shrinks. When a bear rug is done the head is mounted and than it is streached on a board til it is dry. This makes it as large as possible. When it gets wet it is going to shrink a good bit.
For example. I have a Dry tanned Whitetail cape sitting on the couch beside me. If I measure it behind the ears it is 16". When it was fresh off the animal raw it measured 19". Once I rehydrate it, it will measure 19" behind the ears again.
If the mounts dry to slow mold could begin to grow on the hair as well as under the skin.