The g'mara on B'rachot 64a quotes R. Avin Halevi as saying that when we depart from a person we should say "go to peace" (like Yitro to Moshe), not "go in peace" (like David to Avshalom), but that when we depart from the dead we say "go in peace" (based on Psalm 84). A note in my Soncino translation says that this departure from the dead refers to leaving the funeral procession.
I've never learned that I'm supposed to say anything to the meit (dead person) at this point. I'm not part of my local chevra kadisha, so I don't know if any non-psalm speech is involved, but I had thought not. (And anyway, that would be earlier than the note suggests.)
Are we supposed to, essentially, verbally say goodbye to the meit at the end of the funeral procession? If not, did we ever? If not, what is this g'mara referring to?