Chi Omega does have a few "Special Initiates" each year. It is a fairly rare thing. It is intended for women who had certain circumstances that prevented them from membership as a collegian.
Nominations are submitted to the Governing Council (National Officers) and can be sent in by an alumnae chapter, a collegiate chapter or an individual alumna. (Approval of the local alumnae chapter is required.)
The honoree becomes an initiate of an existing chapter i.e., there is not a special chapter designation for these members. As far as describing any aspect of the ceremony itself, that should never be done online, via email etc., whether you are communicating with another Sister or not.
I shared in an earlier thread that my mother was a Special Initiate in 1994 and yes, it was a highlight for me.
ETA: Probably our most "famous" Special Initiate in recent years was NASA astronaut, Susan Helms who was intiated by Pi Gamma Chapter, Univ. of New Mexico.