There is absolutely NO problem in using breeding stock that is line bred !!!!!!! However, one must cull out as many UNWANTED characteristics as possible at the begining of the project, then cull ruthlessly. This is how purebreds are established. Take the Morgan horse breed as an example. Every one of them traces back to the ONE stallion Justin Morgan multiple times. Also, while working at UCD , I took a line of linebred mice and then inbred them ( father x daughter, mother x son ) for 27 generations to get a line that were virtual clones for research before cloning was even possible without any ill effects. I produced the research animals by the hundreds.