I've seen this on several arcade "Switcher" power supplies and don't know what it's for. It's a wire connected from the transformer to ground and the SMPS seems to work whether or not if it's connected.
Picture #1 is the wire connected
Picture #2 is the wire not connected, but PS functioning
Picture #3 is the part of the schematic I believe shows the connection.

Still new to repairing SMPS. Thanks for any help!

 

It is a galvanic or Faraday shield.
Usually connected to Earth GND.

 

I concur with @MaxHeadRoom though the 'ground' here is virtual, being the centre point of a capacitive divider off the AC bridge rectifier, which is the common point of the push-pull ouput stage of the inverter. I very much doubt its physically connected to the external Protective Earth.

 

Also not connected as a continuous loop as shown as this would result in a shorted-turn on the transformer.
Possesses an open circuit loop.

 

Thank you for the informative replies!

 

Also not connected as a continuous loop as shown as this would result in a shorted-turn on the transformer.
Possesses an open circuit loop.

A copper strap or even a length of hookup wire forming a shorted turn around the outside of the transformer can give a shielding effect to contain time varying magnetic fields that might otherwise cause noise problems.