The question is whether the "mission" of the nuns can continue whether they are part of the Church or not. If they reject the Vatican, they can be completely cut off from support from the Church, which means they will have to make up the funding from other sources. Certainly the left wing will fund them, if only to embarrass the Church, so they can survive for a while. Meanwhile the Church can use its money to support people in a way faithful to Church teachings.
But there are limits to all of this. These nuns are getting very old, and one thing they have severely neglected is vocations. Either way, through financial starvation or eventual death, this branch is dying out. And it ought to be in these women's minds that the Church supports nuns in their old age, but they are risking having that cut off.
There are convents which are faithful to the Church and are stable or growing, and are younger. They won't be able to take over these nun's work, but they will survive.
One of my Mothers Cousins was a Sister of Mercy in Halifax, these nut cases drove her from her Vocation. On the good side I have five new Cousins.