Anyone in classical times who took part in a violent rebellion aiming to kill the representatives of public order
forfeited his life if the rebellion failed. To that extent, all those who took part in Jesus’ rebellion were guilty and faced death when Pilate conquered them.
However, Pilate only crucified Jesus and a few other leaders; most of the simple participants were able to go home. In that sense Jesus (and the other leaders) did indeed die on behalf of his many followers.
The statement of faith died for us is based on this historical experience of people who took part in Jesus’ movement.
This experience of the actual representative death of the noble, therefore godlike, Jesus was interpreted in different ways in the early Christian groups. One version was the Persian interpretation of God’s self-sacrifice as known to the groups in the Mithras cult.
This interpretation is expressed in the words explaining the Last Supper in Matt 26:26-28par; This is my body, this is my blood.
Paul and his tradition put it in a similar way: Christ died for us, for our sins: Romans 5:6-8; 1 Cor. 15:3.