Suppose you use a GFCI device to allow use of grounding receptacles on a non-grounded circuit. Now, suppose you want to add a receptacle or two. You would use NM cable, which has a ground. You should not connect the ground wires to any receptacles or other ground wires. Clip them off.
Suppose an internal hot wire energized the external metal parts of a load with a grounding plug. If you connect the ground between two receptacles, the metal parts of a second load with a grounding plug would also become energized, interconnected by the ground wire in the new cable.