When can your character's HP reach one? Only in battle? Outside of battle?
If only in battle, use troop events, which allow you to trigger them based on an actor's HP.
If outside of battle (and I don't like this idea), use a parallel processing common event to continually check the actor's HP. If it's 1, turn on a switch. If it's not 1, turn the switch off. Add a Wait 10 frames or something at the start so it's not doing it 60 times a second. Then condition your other common event by that switch.