Albert Barnes Commentary Numbers 19:10

"And he that gathereth the ashes of the heifer shall wash his clothes, and be unclean until the even: and it shall be unto the children of Israel, and unto the stranger that sojourneth among them, for a statute for ever." — Numbers 19:10 (ASV)

The one who gathered the ashes became equally unclean with the others. For the defilement of the people, previously transferred to the heifer, was regarded as concentrated in the ashes.