Leviticus 16:32

“And the priest, who shall be anointed and who shall be consecrated to be priest in his father's stead, shall make the atonement, and shall put on the linen garments, even the holy garments,”

The responsibility for the maintenance of this ritual lay with each descendant of the High Priest who took on his office. The one who was anointed and consecrated in his father's place would be the one who had to make atonement and would be permitted to put on the especially holy garments, the linen garments. But sometimes it would require a deputy, because of possible illness or infirmity, or because in some way the High Priest became unclean in such a way that there was not time for him to be made clean. For the laws of uncleanness applied to him as much as to all. By the time of Jesus elaborate precautions were taken to prevent this happening.