Dogs that bite are not necessarily doomed to be put to sleep. There are so many varying degrees of placing the teeth onto human skin or clothing, and the intent behind such an action can also vary greatly. In my view it's not acceptable for teeth to touch clothes or skin at all at any time. This is a simple black and white rule (dogs like black and white rules as they're easy to comprehend) that all family members and of course the dog can come to understand.
Many dogs express themselves with their mouths as it is the front most part of the body that interacts with either other people or dogs. Being taught bite inhibition should start at an early age so that the dog learns that use of the mouth and teeth is not rewarding or acceptable as a means of play with people. Acceptable mouthing with another family dog is fine, though this too should be supervised.
The word nipping is normally associated with puppies. Puppies can be surprisingly hard mouthed when they arrive at your home, this can be a result of rough play with siblings in the litter pack. Sometimes this is unwittingly encouraged by tug type games with children in the new home, or dads that like to rough it up with the young dog.
Teach the puppy calmness and good manners and this will become the norm. If not correctly addressed, nipping and rough behaviour can progress into biting, and then the biting can be hard and holding onto skin or clothing. In any event, it is wise to address these issues early on to prevent unwanted progression.