|   This is his security Blanket 
  I would not worry about your dog going to sleep with his mouth on the bed.  My brother has a dog that has done this since a puppy, he is 12 years old and still does it.  The Vet told them it was like a child with a security blanket or a favorite toy that they snuggle up to when going to sleep.  It makes him feel secure and safe.  You are great for rescuing this puppy.  
 One of our "no kill"  shelters here gives each new puppy a toy to be in their cage with.  They become attached to this and it goes to their new home with them.  Maybe this happened to him at the shelter????
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