No, a stop spell means you are unable to move, being frozen in time.

For the most of the part, characters are either KOed or "wounded" (which probably means too wounded to participate in battle).

When all your members die, you get game over because the other party members are usually not around. You usually have to enter an airship or another place where the other members hang out, or make a phone call, to change members. With everyone KOed, no one would be able to get there in time, and they would get eaten.