This old saying in the Order is because of the great devotion Dominicans have always had in praying for the faithful departed. This old phrases goes this way: "It's a good thing to be a live Francisican, a dying Jesuit and a dead Dominican." The faithful used to want to be associated with the Order as members of the "3rd Order" specifically because of the dedication the Order has to remembering the dead in our prayers.
While the Church gives us this month of November to especially remember our departed and by our penances, prayers and the Holy Sacrifice of the Mass to help them come more quickly before the Face of God, throughout the year, Dominicans are especially committed to remember those who in life have helped us and so now, we in turn try to help them!
Everyday before processing into the refectory we pray the De Profundis for our departed friends and benefactors. Without them our life would not be possible! Again in the evening after Compline we pray for all the faithful departed again praying the De Profundis. In the old days, at this time the passing bell would be rung to remind the faithful to pray for the dead.
Every week, usually on Mondays, Holy Mass is offered for the dead, and especially all those enrolled in our Perpetual Prayer Society. Whenever a Friar dies, all the friars offer Mass for him (3 Masses?) and when a nun dies each Sister must offer suffrages for her soul by reciting either the Rosary or the 7 Psalms. The same is offered by each nun on the death of the Supreme Pontiff, the bishop of the diocese and the Master or ex-Master of the Order.
Throughout the year there are special days when we remember our parents (February 7th), our brothers and sisters in the Order (November 8th), and our relatives and friends and benefactors (September 5th). The Holy Sacrifice is offered and the Office of the Dead is said in place of the Office of the day.
Once a week, usually on Tuesdays, we recite the "Seven Penitential Psalms" in Choir asking "God, giver of pardon and author of human salvation: we beseech your loving kindness that through the intercession of blessed Mary, ever-virgin, and of all your saints, you would grant that the brethren, sisters, kinsfolk and benefactors of our Order who have passed out of this life, may reach the fellowship of everlasting happiness."
To pray for the Holy Souls in Purgatory is one of the greatest acts of charity we can perform for they can't pray for themselves. We especially should remember those who have no one to pray for them. You can be sure that once we die we will have a host of powerful intercessors praying for us in Heaven! Truly the doctrine of the Communion of Saints is an image of Trinitarian Communion and one of God's wonderful gifts to us!