No Ground Wire In Outlet Box
Some homes without the ground wire, may be wired with BX or armored cable. This is the cable with the flexible metal casing around the wire. If this is the supply to your outlets, and it runs from your metal boxes all the way to your entrance box (where your fuses are), you are in luck. The outer casing of this wire can serve as the ground.
Generally, NO. Without a ground wire attached to the box, attaching a ground wire from the outlet to the box is useless. It would only be acceptable if the box were connected to the building ground through metal conduit. To ensure that the conduit is properly connected, a ground bond test should be performed.
This is how Ground is provided at every outlet box in the house. And in all of these, NOTHING (except a Ground lead) should be connected to that Ground, so it never carries any current under normal circumstances. In older systems there was no Ground lead extending beyond the main fuse box, and no Ground bus in the box.
The junction box will have a green screw. Screw the ground wire to this as it connects to a tapped threaded hole on the back side of the junction box. If there's no screw, there should be a grounding clip. This secures the ground wire to the edge of the metal junction box.
In older homes open grounds are quite commonly found, this is due to the original wiring systems not being upgraded to a three wire system or only selective areas being upgraded. The methods of grounding these receptacles vary greatly dependent on the period when they were installed or upgraded. A grounded Outlet.
Contact between an attached device (such as a light switch or outlet) and the metal box completes the grounding contact. Romex or NM wiring can be used with metal electrical boxes when the bare or green grounding wire is attached to the box by a screw.