They are known as lawsuit guitars because they are of such good quality (often matching or even surpassing the original Fenders and Gibsons they replicate), that:
Around 1981, though, Fender, Gibson, Rickenbacker and a few other US guitar manufacturers got their hands on some “lawsuit” guitars made in Japan and quickly threatened to sue when they saw how exact the Japanese replicas really were. The Japanese replica-making guitar manufacturers were forced to stop making these “copy” guitars around 1983.
There are still tons of these guitars around if you search the used guitar shops and pawn shops, although some of the more famous models outprice the American equivalents they were originally based on!
Read more about the lawsuit guitars on this site.