to live through; to survive
祖母は戦争を生き抜いた。
My grandmother lived through the war.
厳しい環境を生き抜いてこそ強くなれる。
You can only grow strong by surviving harsh conditions.
もしあの災害を生き抜いたら何をしたい？
If you survived that disaster, what would you want to do?