Once we get past the grossness factor, there are a couple of reasons for this behavior. First, the contents of a used tissue are often very salty and this can be tasty…. at least to a dog! Second, dogs like to shred things putting their paws on their slain prey and ripping out chunks of flesh; holding down a crumpled piece of tissue and ripping chunks out of it is similar behavior and the next step is obviously eating it.
Fortunately, this behavior does not mean that your dog is deficient in any nutrients.
If your dog is deficient in anything, eating tissues says he or she may be deficient in a little bit of extra playtime!