Characters can be both petrified or time stopped by certain attacks.
Some enemies can inflict Gradual Petrify on the character, which starts a counter. The character can still fight and as the timer runs down, the afflicted unit's resistance to physical attacks gradually increases, rendering them almost immune to such attacks when the countdown reaches 1, but once the timer runs out, the character turns to Stone and dissapears from the screen. It can be cured with Esuna, by Stona (spell), a Gold Needle, or a Remedy.
Certain spells also inflict the Stop-status effect, which freezes the character completely for a certain amount of time. It also stops other status effects like Doom or Gradual Petrify. Stop can be removed by a Chronos Tear or the Dispel-spell.