Regarding the persons involved in Christ's death, namely the Father, Son, and Holy Spirit, we may say that death is part of the Trinity because in Holy Saturday Jesus is dead. Death is taken into the Trinity's life. And the experience of the death of another and memory of that dead one is also part of God in that the Father endures the death of his Son. And vice versa, since these two persons share fully in each other's lives, death is now a part of God, and the knowledge of absence of another in death is a part of Jesus resurrected life. And furthermore, we participate in this death and life because through the gospel we participate in the life of the Trinity. It is no longer I that live, but Christ who lives in me. It is no longer I who die, but Christ who dies.
But I am incapable of thinking through clearly the Spirit's role in all of this. It is a lacuna for me.