They won’t go near a dead person to make themselves unclean. But they may make themselves unclean if the dead person is their father, mother, son, daughter, brother, or a sister that is not married.
“If any of Aaron’s descendants [386] has one of the bad skin diseases [387] or a discharge [388] he can’t eat the holy food until he becomes clean. [389] That rule is for any priest that becomes unclean. [390] That priest can become unclean from a dead body or from his own semen. [391]