What is the ruling on a ritually impure person (junub) walking to bury a deceased person if he is unable to perform ghusl?

There is no harm for a person in a state of major ritual impurity (junub) to follow a funeral procession and bury the deceased, as ritual purity (tahara) from minor or major impurity is not a condition for this. Rather, purity is only a condition for performing the funeral prayer.

As for the Hadith: "Is there among you a man who has not committed a sin tonight?" its meaning is either that he has not committed a sin, or that he has not had intercourse that night. If the latter, then it does not stipulate purity; rather, it is preferable for the one who undertakes the burial not to have had intercourse with his wife that night, as he would then be far removed from worldly pleasures.