This is where the definition of eternal life is so important. Jesus told us what eternal life is, it's not existing forever, that's not the definition. It's knowing God, and knowing Jesus.
Relationship with God is life, and we live in Him, so we have eternal life. As long as He lives, we live in Him.
Those who do not know God, and know Jesus, do not have eternal life, yet though they exist.
Having eternal life and not having eternal life are not functions of whether the person exists. They can exist without having eternal life, not knowing God.
The question of whether a person continues forever in torment or not must be answered separately.
Much love!
Mark