I believe you could also just put in a GFI outlet or circuit breaker
to give you protection from the ungrounded wiring. That's what happened
in my house. I had some circuits on ungrounded 12 and 14 gauge Romex
and it was too much of a pain to re-run it, so when I had my service
panel changed to 200 Amps, we put in GFI circuit breakers. It is
allowed under code.