Even to a woman

Ralph of Shrewsbury, Bishop of Bath and Wells, January 1349:

The contagious pestilence of the present day, which is spreading far and wide, has left many parish churches and other livings in our diocese without parson or priest to care for their parishioners. Since no priests can be found who are willing, whether out of zeal and devotion or in exchange for a stipend, to take on the pastoral care of these aforesaid places, nor to visit the sick and administers to them the Sacraments of the Church (perhaps for fear of infection and contagion), we understand that many people are dying without the Sacrament of Penance. These people have no idea what recourses are open to them in such a case of need and believe that, whatever the straits they may be in, no confession of their sins is useful or meritorious unless it is made to a duly ordained priest. We, therefore, wishing, as is our duty, to provide for the salvation of souls and to bring back from their paths of error those who have wandered, do strictly enjoin and command on the oath of obedience that you have sworn to us, you, the rectors, vicars and parish priests in all your churches, and you, the deans elsewhere in your deaneries where the comfort of a priest is denied the people, that, either yourselves or through some other person you should at once publicly command and persuade all men, in particular those who are now sick or should fall sick in the future, that, if they are on the point of death and can not secure the services of a priest, then they should make confession to each other, as is permitted in the teaching of the Apostles, whether to a layman or, if no man is present, then even to a woman.

Quoted in Philip Ziegler, The Black Death.

Adds Ziegler:

The authority to hear confession has, in all periods of the Church’s history, been restricted to the priesthood. To throw it open to laymen and even to women, though not in defiance of canonical authority, was a step to be taken only in case of extreme emergency. It was a confession on the part of the Church that the crisis was out of control and the normal machinery no longer able to cope with it.

Though Ziegler's volume was published in 1969 and there have been many other books on the subject since that time, it remains highly readable and in print. A young man when he wrote it, the author has gone on to write numerous other books and is still alive as of this writing.