Dear MJM,
So long as a marriage has not been declared null by the Church, that marriage is considered to be valid and the man and woman are still considered to by married sacramentally. The Church allows divorced Catholics to receive Holy Communion if they are living a chaste, celibate life. If they attempt to re-marry outside the Church or if they are sexually promiscuous, then they may not. See the Catechism of the Catholic Church #1649, #1650.
Fr. Vincent Serpa, O.P.