The story
* Unknown, but possibly from shoad (“loose stone and rubble; fragments”), equivalent to shoad + -y; 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.
Etymology from Wiktionary, CC BY-SA 4.0.