Religious congregations of non-virgins?
I am not a 100% sure, but I have a strong suspicion that he may be making a reference to the religious congregation known as the Dominican Sisters of Bethany.
Several years ago, I had the grace of attending a retreat that was preached en français while I was living in France. The Dominican priest, who preached the retreat happened to be the postulator of the cause for beatification of a certain Fr.Jean-Joseph Lataste (1832-1866), who has since been beatified on June 3, 2012, by Pope Benedict XVI.
Blessed Jean-Joseph Lataste (1832-1866)
Following a sermon he delivered in a female prison in Cadillac, Gironde on 14 September 1864 he felt that the Lord called him to establish a religious congregation to cater to the needs of women who left prisons or who were abused. In 1865 he started to formulate ideas in order to begin this mammoth task and he recruited prospective members for this new institution on 14 August 1866. He established the order in 1867. - Alcide-Vital Lataste
Fr. Lataste’s new congregation was unique in many ways. It was designed for women of ill-repute and was very austere in the beginning. These women lived a life of penance rarely seen in Religious Orders of those times: fasting, walking bare foot all day, never looking a visitor in the face, keeping their eyes fixed on the ground and almost perpetual silence were observed in their convents. A life of contemplation was their end goal.
These so called inmates became great contemplates and I am sure that some day some of the founders may eventually become canonized.
The congregation is somewhat different nowadays.
Our congregation began when a young French Dominican had an experience that turned his life upside down. Fr. Jean-Joseph (Alcide) Lataste was 32 years old when he was sent to give retreats in his hometown of Cadillac near Bordeaux in the south of France — in a women's prison.
There were 400 prisoners, many of whom had been raped by their boss, become pregnant and murdered their child. Most of them had no place in society on their release — only the law of rehabilitation. After release, the ex-prisoners entered a long time of "rehabilitation" to see if they had changed. Only then did the prisoner regain her civil rights — or not. Since it was assumed that the women remained dangerous during the time of rehabilitation, most were deported to the colonies of Guyana and Cayenne.
When Lataste started the first sermon of his retreat in 1864, he did something unusual: He looked at the women. He saw them as children of God, and began his sermon with the words, "My dear sisters." Unheard of!
Touched by this himself, he changed his sermons, and had deep spiritual experiences. For example, almost all the women — tired as they were after a day of forced labor — gave up their precious night's sleep to take part in night worship. He was deeply touched to think that God, who remained in the sacrament all night, did not consider himself to be too great to remain in the midst of these women. When God thinks and acts in this way, how can we reject people like these prisoners?
Lataste wanted more than a four-day retreat: He developed a vision for a house where women could live as sisters regardless of their past. A house where each would stand up for the others, and lift up her sisters. The idea for Bethany was born.
He loved the story of Bethany, where Jesus' friends Martha, Mary and Lazarus lived. Some equated this Mary with Mary Magdalene, who had been a sinner, and Lataste followed the view of Magdalene that was common at the time. Jesus loved to visit their home, and seemed to prefer Mary, telling Martha that Mary "has chosen the 'better part' and it is not to be taken from her" (Luke 10:42). Regardless, Mary Magdalene shows us that the greatest sinners can become the greatest saints.
In the time of Lataste, there existed shelters where women who had nowhere else to go lived lives of penance and humiliation next to monasteries of exemplary sisters. Sometimes that was their only chance not to end up in prison again.
But Lataste wanted more. He wanted a real community, a home, for people with a past. He envisioned a community where everyone could be the same. The outside world would not be allowed to know where someone came from. Those from good middle-class homes, with good reputations, would be equal to someone who had been in prison as a thief. Once a journalist asked a group of sisters if the ones who "had a past" could stand up. And the whole group stood up.
Our congregation has official permission from the Church to admit women who legally cannot enter the congregation, (e.g. if they are married). Even today, these women cannot take a vow. That is why we do not take a temporary vow in Bethany. All sisters make a kind of temporary commitment and commit themselves to the congregation for three years. This is a big legal difference, and in this way the outside world can't tell who came to Bethany on which path. Only when it is time for perpetual vows do we make our profession. - Bethany: The story of a unique congregation
Whether or not Fr. Lafetur is referring to this type of congregation or not, it seems to fit the perimeters of your question. I am sure others examples are out there; I am simply unaware of them.
Interestingly enough the original Dominican Order of Nuns was formed by a group of women from the Cathar heresy who, accepting St. Dominic’s preaching and lifestyle, gathered in Prouilhe, in the south of France, and formed the first community of Dominican nuns.