If a creature's power is reduced to 0 or less by a continuous effect, does it die?

A creature dies from lethal damage or from having toughness reduced to 0 or less — not from having its power reduced. Power represents how much damage a creature deals; toughness represents how much damage it can survive. These are governed by different rules.

Under CR 704.5f, a creature is put into its owner's graveyard as a state-based action if it has toughness 0 or less. CR 704.5g handles creatures with lethal damage (damage equal to or greater than their toughness). Neither rule mentions power being 0 or less as a cause of death.

Power can freely be 0 or even negative without threatening the creature's survival at all. A creature with 0 or negative power simply deals 0 damage when it attacks or blocks (damage cannot be less than 0 for assignment purposes), but it remains on the battlefield.

Example: Your opponent controls a 2/2 Bear. You cast a spell that gives it −3/+0 until end of turn, making it a −1/2. The Bear's power is now −1, but its toughness is still 2. No state-based action removes it; it survives the turn perfectly fine, just unable to deal damage.

If instead the effect gave −3/−3, the Bear would become a −1/−1, and state-based actions under CR 704.5f would immediately put it into the graveyard because its toughness dropped to −1 (less than 0).