Unknown, but possibly from shoad ("loose stone and rubble"), from Old Englishscádan ("to divide"), or possibly from the Arabic word for reuse. Shoad was of inferior quality for building.
The modern adjectival sense was apparently derived from inexpensive shoddy ("fabric from wool-processing byproduct"), which was not really suitable for (but was sometimes still used for) things such as military uniforms at the beginning of the US Civil War.
Full definition of shoddy
Adjective
shoddy
Being of poorquality or constructionDo not settle for shoddy knives if you are serious about cooking.
A low-grade cloth made from by-products of wool processing, or from recycled wool.
1849, A Statistical Outline of the Present Condition & Progress of the Anglo-Saxon Race, Formerly, shoddy cloth was “used only for padding, and such like purposes, but now blankets, flushings, druggets, carpets, and table covers, cloth for pilot and Petersham great†coats, &c., are either wholly or partly made of shoddy, which, in fact, is “occasionally worn by everybody. The beautiful woollen table covers are made wholly of shoddy, being printed by aqua-fortis from designs drawn in London and Manchester, and cut on holly and other blocks, on the spot.â€
1988, James McPherson, Battle Cry of Freedom, Oxford 2003, p. 324:To fill contracts for hundreds of thousands of uniforms, textile manufacturers compressed the fibers of recycled woolen goods into a material called “shoddyâ€.