It depends on the size and the location. After both world wars plenty of people had odd bits of shrapnel wandering about inside them for years, because it would be too difficult or dangerous to get it out.
We had a dog who carried a few shotgun pellets inside her, shallowly enough for one to feel one of them under her skin. No point in subjecting the dog to the stress of an operation.
But with a bullet bullet, the size means that it would be almost certainly worth trying to get it out. Again, depending a bit on location and how much trouble it's causing. Abdominal cavity = one answer, muscle = another.