Unfortunately, some families and individuals do not call the parish for a priest until after their loved one has died. The rite foresees this unfortunate option:
263. When a priest has been called to attend a person who is already dead, he is not to administer the sacrament of anointing. Instead, he should pray for the dead person, asking that God forgive his or her sins and graciously receive him or her into the kingdom. It is appropriate that he lead the family and friends, if they are present, in some of the prayers suggested at the end of the “Commendation of the Dying,” as already mentioned. Sometimes the priest may find it necessary to explain to the family of the person who has died that sacraments are celebrated for the living, not for the dead, and that the dead are effectively helped by the prayers of the living.
Note the value attached to participation by the mourners of the dead: the priest leads the loved ones and friends in some of the prayers given in the rite. The rite assumes that this prayer will be a comfortable one, perhaps for people who experience a disconnect from the Church–one that may have delayed their call for a priest. It would seem the litany form might ease inexperienced people in to the moment of prayer.
Most difficult for the priest would be the situation in which he finds himself confronted by a possibly angry family expecting him to anoint, and give pardon and communion to an obviously-dead person. In that case, I don’t think the wording above will calm concerns. The PCS rite has lots of prayers and readings. The body may be sprinkled with holy water (PCS 225). Most families would be satisfied with something substantive.
If there is doubt about death, however, the Church is prepared here, too:
If the priest has reason to believe that the person is still living, he may anoint him or her conditionally. In this case, the sacramental form is introduced with the words: “If life is in you: …”