This status when inflicted stops the target's ATB bar and a few other timers.
All timers stop... Poison, Sleep, Paralysis, Regen, HP Leak, Count/Doom, Reflect/Wall, Poison, Gradual Petrification.
These timers continue when Stop status is removed.
However, in the SNES version, Sleep, Paralysis, Regen, HP Leak (for characters), and Gradual Petrification timers are not restarted. Regen benefits most from this bug. However the other statuses, excluding HP Leak and Regen, will cause the game to act strangely and/or freeze when used on enemies.
Inflicting Stop status on Stop resets/changes the timer.
Edit: Updated info.