How about using stasis chambers for the brig? The inmate could not even attempt an escape. Considering how boring it must be to sit alone in a cell in the brig, I think that as an inmate I would like to be unaware of the passage of time. Win-win.
Well if you're punishing a crew member, you'd want them to experience the passage of time to think about whatever crime it was they commited, unless people in the 24th Century consider just the fact that some of their time 'dissappeared' bad enough, rather than being conciously aware of not doing anything.
If there's a shipwide power failure, I guess that there are systems that have some form of capacitor to keep vital systems going until main power if (hopefully) restored. Presumably brig force fields would be one of these systems.