As we remember Christ, just as through the eucharist, we remember that we become Christ. Rob Bell says in Jesus wants to Save Christians that the "given over" is important here. Paul is speaking of the healing in the world and how when we identify with the suffering of our neighbor and we commit ourselves to doing something about it, it will cost us something.
So then, death is at work in us, but life is at work in you. 2 Corinthians 4:12
That's how the eucharist works. For someone to receive, someone has to give... the church is the living eucharist.