Unquestionably, those religious men and women who are under the Rule of St. Benedictine have taken, among other vows, the vow of Stability. That is, they are in a religious order that is cloistered; in other words, they have taken a vow to never leave their abbeys, and to not travel. Instead, they are to devote their lives to prayer and service to God. This renunciation of the urge to travel is meant to effect "conversion of the spirit from secular concerns to union with God." In fact, Canterbury was an early Benedictine monastery which was devoted to prayer.
The pilgrims who are from the Benedictine orders are the Friar, the Monk, and the Prioress. These characters act as vehicles of Chaucer's satire of the corruption of the Catholic Church which at the time was involved in the removal of the papacy at Avignon, France [the Western Schism], noted for the corruption of the papal curia's efforts to increase its revenue and for its corrupting secularism. Certainly, these characters of Chaucer do not take their vows of poverty and stability--even chastity with some--seriously. In "The General Prologue," for example, Chaucer intimates that the "saintly" lives of those in religious orders is anything but what it should be as, for instance, with the description of the Friar,
...he was not like a cloistered monk
With a threadbare cope, like a poor scholar,
But he was like a master of arts or a pope.
Of wide (expensive) cloth was his short cloak,
Which was round as a bell fresh from the clothespress. (259-263)
The Monk has his sleeves trimmed "with lovely gray fur" and is much too manly in his activities: He owns horses and greyhounds, and he hunts, "Daily riding out of his monastery" and he is given to "much ignoring of his orders" because he
... much preferred to let
The strict and ancient Benedictine Rule
Go sliding by; he favored the brand-new school,
Open to all that grew up high in this world. (173-176)
The Prioress [Nun] seems reverent enough, as her smile is "mild and unpretentious," but when she prays and sings, she "chants"
...through her nose in proper style,
Much like her full and flowing French, acquired
From English teachers at Stratford on the Bow (122-125)
While she tries to be courtly, the Prioress, affecting daintiness as she speaks in French, with her large forehead and vanity beads around her neck, rather than the traditional rosary, it is clear that she is not what she should be.