Line breeding means:"The mating of related animals less closely related than inbreeding."
Line breeders usually breed out every couple of generations to similar, but unrelated, line-bred dogs. This greatly diminishes the possibility of the 'deleterious effects' of inbreeding and overcomes breeding 'drag' - the tendency toward average over several generations.
Actually there seems to be no agreement among sporting dog breeders about where the line between inbreeding and line breeding is, exactly. There have been a number of very healthy and successful field trial dogs with COIs as high as 16.5. The average competitive setter is probably closer to 3.0 to 6.5 COI. I have one that has a 10 generation COI of 12.0 and is a very fine animal.
Line breeders do not breed brother to sister as an inbreeder might. They may breed a sire to a littermate's offspring to better fix characteristics that they value. The effects of in-breeding and at what level of COI they are manifested in dogs is not well explored with performance dogs that are bred and culled by breeders.
Carolina wild dogs are a small population that has apparently bred in the wild for many hundreds of years. As long as Darwinian principles are at work there appear to be no deleterious effects of inbreeding in this small population.
A useful discussion of Canine genetics by Dr. Jerold Bell, which defines out-breeding, line breeding and inbreeding may be found HERE
2 days ago