From a CNA/EWTN News piece, quoting Ann Carey:
Carey
said that after Vatican II, members of many religious orders began to
live in apartments and find their own jobs, separate from a corporate
apostolate such as teaching or care for the sick.
In addition, they threw off the “loyalty and faithfulness to the
Church” as well as the “deference to the hierarchy” that had previously
characterized religious life.
The changes were so drastic that they caused some women to leave the
LCWR, Carey said. These women formed another group, which eventually
became an alternative superiors’ conference known as the Council of
Major Superiors of Women Religious.
This more traditional group, which requires its members to adhere to
the essentials of religious life as understood by the Church, is
attracting the bulk of young vocations today, she noted.
If the conference is to undergo a true renewal, Carey said, its members
must re-examine the Church’s understanding of religious life and make a
firm commitment to live as “representatives of the Church,” in union
with the local bishop.
She emphasized that the Congregation for the Doctrine of the Faith is
not trying to return to the pre-Vatican II days but is instead promoting
an “accurate interpretation of those documents” and the life they
portray.
Carey said it will be “very interesting to watch” as the situation
progresses. While she does not know what will happen, she said there are
ultimately only two possible outcomes.
It is possible that the LCWR will cooperate with the Vatican’s reform
efforts and see that they have gotten away from Church teaching, she
explained.
However, she is unsure whether that will happen, because some of the
group’s members are “very convicted that what they’re doing is the right
thing.”
The other option is for the conference to relinquish its canonical
status and simply continue as a professional group, which Carey believes
will cause them to “lose a lot of their members.”
Read the entire piece.
My guess is that the LCWR will double down and try, for a while, to win
a public relations battle, benefiting from the mostly positive spin in
the media. But, eventually, the LCWR will most likely lose its canonical
status and try to continue on as a sort of alternative, non-official
"conference". It is very hard to see the LCWR full cooperating, especially since its identity and agenda, from its founding forty years ago, have been almost unremittingly contrary to Church authority and in opposition to many key Church teachings.