To live "in Christ" is to live in a mystery equal to that of the Incarnation and similar to it. (New Seeds of Contemplation, 158)
Thus a new incarnation of Christ takes place in christians, which is synonymous with a resurrection from the death on the cross. The new self carries the wounds of Christ on the body: the remembrance of the misery of sin out of which the soul was awakened to a blessed life, and a reminder of the price that had to be paid for that. The pain of yearning for the fullness of life persists until, through the door of actual physical death, entrance into the shadowless light is gained. (The Science of the Cross, trans. Josephine Koeppel, OCD)
The Risen Lord continued to bear the wounds of the Crucified Christ. In the same way, the wounds of sin remain in the redemption-in-process that is the humanity of the Christian. For better or for worse, nothing makes us who we are more than our suffering. We find ourselves as human beings in an injured state, often foiled by our own faults and sins and subjected to misery because of the sins of others. This is the mystery of the effects of original sin in the world.
God redeems us in Christ by meeting us exactly in this miserable and alienated condition: This is the mystery of Christ crucified. Though killed in his human nature, death could not contain Christ as God. Thus the Cross blazes a new path for the humanity he shares with us, a path out of the deathly misery we have insisted upon for ourselves with our sins to a new and risen life.
As we become redeemed by consenting to let our own humanity be drawn into the humanity of Christ--and this is the mystery of baptism and Holy Communion, by the way--the wounds and broken parts of ourselves remain, but in a transformed way. Though freed and redeemed, our sufferings and struggles are still the things that have made us who we are. But these wounds, previously just a source of meaninglessness and pain, have been transformed into stigmata, signs of transformed suffering that illustrate to those around us the possibility of resurrected humanity.
Thus, in a sense every Christian is a stigmatic. But it's not that we 'receive' the stigmata, for the wounds have always been there. The hurts and brokenness that were meaningless and so often a source of the desperate cycles of violence of the world that does not know God, have now been transformed into the redeemed wounds that bleed only compassion.