The earth wire typically is connected to the metal casing of the appliance, and the earth pin of the plug. This is a critical safety feature, which will cause the circuit protection to trip in the event of phase touching the metal of an appliance.

Connecting phase directly to the metal is an excellent way to kill someone.

https://www.rnz.co.nz/news/national/502326/nelson-electrician-stephen-burton-s-failure-to-carry-out-simple-task-linked-to-death-of-builder-craig-johnston

First, both 'neutral' and 'ground' are leaving that plug.

Second, that 'ground' wire is connected to both live and neutral, with no actual ground connection present. The other end of that wire is presumably connected to the exposed metal of the appliance this plug would be powering. Just calling a wire 'ground' doesn't make it ground nor safe; it has to actually be electrically connected to a grounded point.