John Lightfoot on John 11:55

[To purify themselves.] "R. Isaac saith, Every man is bound to purify himself for the feast." Now there were several measures of time for purifying. He that was unclean by the touch of a dead body required a whole week's time, that he might be sprinkled with the water of purification mixed with the ashes of the red heifer, burnt the third and the seventh days.

Other purifyings were speedilier performed: amongst others, shaving themselves and washing their garments were accounted necessary, and within the laws of purifying. "These shave themselves within the feast: he who cometh from a heathen country, or from captivity, or from prison. Also he who hath been excommunicated, but now absolved by the wise men. These same also wash their garments within the feast."

It is supposed that these were detained by some necessity of affairs, that they could not wash and be shaved before the feast; for these things were of right to be performed before, lest any should, by any means, approach polluted unto the celebration of this feast; but if, by some necessity, they were hindered from doing it before, then it was done on a common day of the feast, viz. after the first day of the feast.