In this situation, why is the existing (reduced) equipment grounding conductor better than none? The whole circuit is protected by a GFCI, which will trip faster than the breaker will, in the event of a ground fault. That is it's function. IMOI, I would think the reduced egc is equal to no egc. Don't use it.

If you are talking about a non-gfci protected circuit, then, yes the reduced egc is preferred to none.
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Rick Miell