Hanna-Barbara Gerl-Falkovitz in the Tagesspost (acknowledgement to Kath.net) has asked that the church consider the possibility of opening the diaconate to women. Gerl-Falkovitz is a professor of the philosophy of religion at the Technical University of Dresden. I have heard her speak at the International Institute of Culture’s seminars in Eichstaett, Germany. She is known for her orthodoxy and loyalty to the magisterium.
She proposes that the Church consider an order of women who had earned true holiness through prayer and service (not through academic degrees). These women would have the special role, mostly in hospitals, of accompanying the sick and dying. They would also under certain circumstances have the ability to give the sacrament of the sick, “unter bestimmten Umständen auch die Krankensalbung zu spenden.”
This latter part of her proposal depends on the decision of the Church as to whether the priest is the ordinary minister of the Sacrament of the Sick (as he is of baptism) or the necessary minister (as he is of the Eucharist). A layperson (and indeed even an unbaptized person) can administer baptism is cases of necessity. I do not believe the question about who can administer the sacrament of the sick has ever been asked. The relevant verse in James seems to limit the sacrament to the elders (πρεσβυτερους – priests) of the Church:
Is anyone among you sick? Then he must call for the elders of the church and they are to pray over him, anointing him with oil in the name of the Lord; and the prayer offered in faith will restore the one who is sick, and the Lord will raise him up, and if he has committed sins, they will be forgiven him.