What happens to Cessna electric flaps that are moving when power is lost? On final in a C182T you move the flap control arm from 20 to FULL, and when halfway there, the breaker pops (or BUS1 fails, a wire falls off, etc.)

Does the flap stay where it is, slide back to 20°, slide back to UP, or something else? Perhaps the question is “are the stops mechanically significant?”

Would the answer change if instead of blackout it was a brownout? I.e. the motor is still trying to run, but doesn’t have all of its normal oomph.
Stays where it is. The mechanism is a leadscrew and like most leadscrews it's "self-locking", which means that it's held in position by frictional forces whenever the motor isn't turning and it can't be back-driven even by substantial loads. The 20 degree (etc) "stops" are just reference positions for which aircraft performance and load limit data have been determined.