Preventive, not curative
Yakuyoke is protection against misfortune rather than relief from it, and that distinction runs through the whole category. You do not come here because something went wrong. You come because you are entering a period in which something might.
The period is usually a yakudoshi — an age traditionally considered dangerous. The main ones are 25, 42 and 61 for men and 19, 33 and 37 for women, counted in the old system where you are one at birth, and each is bracketed by a preceding and following year that also count. Forty-two for men and thirty-three for women are the taiyaku, the great ones. Shrines publish a table of the current year's yakudoshi ages, usually near the entrance, and you will see people checking it.
Whether you believe any of this is beside the point for a visitor. What matters is that it explains what you are looking at: the person receiving a formal purification in the hall on an ordinary Tuesday is very likely marking one of these years.
What is actually done
Yakuyoke is one of the categories where the informal bow at the offering box is genuinely the lesser form. The proper act is yakubarai — a purification performed by a priest, with the harai-gushi wand, inside the hall. It is bookable at most shrines for a few thousand yen.
Some shrines add something specific. Koami Jinja's whole kyoun-yakuyoke reputation rests on two documented survivals — the priest who escaped the 1923 earthquake carrying the sacred objects, and the shrine taking no damage in the 1945 air raids. Kashima Jingu's is martial: this is the kami of the sword, and warding off misfortune there has the flavour of facing it down rather than avoiding it.
