Fingers can be saved after a severe injury. Factors including the type of injury, the zone of injury, where the fingers are injured with respect to the palm, how long it has been since the injury, the age and health and habits of the injured, (very advanced age, poor circulation and smoking are harder to overcome) and many other factors are taken into account. Whether they are "attached by bone" or just by a skin bridge is relative as well as near complete injures where nerve, artery, tendon, bone and vein are severed are more extreme injuries than just injury to one side of the finger. Cleaner cut injury with a sharp thin blade verses a power saw injury with a thick blade are better. Avulsion and tearing injuries are the hardest to repair. Anyone with an injury such as this would go to an Emergency Room right away to be seen and possibly transferred to a facility where this type of surgery is done. Never immerse a severed finger in water, wrap it in a clean moist glaze, and place in a plastic bag and put that bag on ice. DO not ice directly to the severed finger or part.