Grounded Field Winding

Well, that would depend upon the contents of the detailed electrical design documents with regard to any neutral connection, which documentation cannot be seen from here.

If there were no neutral to <...ground...> connection, then the first fault would not cause damage, though it might prove inconvenient, embarrassing, uncomfortable, or some combination of them. A guess might suggest that having two parts of the <...field winding...> both connected to <...ground...> would introduce heavy circulating currents through those connections and the <...field winding...> that might damage things considerably, and it would be better to trip on the fault than for the damaging situation to continue for longer than the trip operating time.

When I was an engineering student on a co-op assignment at a major generating station, I posed the same question to my manager. His answer was simple and perfectly logically, "Continuity of service". Rather than an immediate trip which would suddenly remove 600MW of generation from service, the operators were alerted to the ground fault, and could perform an orderly shutdown of the unit without affecting any customers.

My followup question was obvious, "what about a second ground fault?". His answer, "It's unlikely that a second fault will occur before we take the unit out of service, but if it does, we're already prepared for the trip."

One ground fault may or may not let out the magic smoke eventually depending on where the fault occurs.

Two ground faults are guaranteed to let out the magic smoke in the very near future.