You must have mis-interpreted something from your sister. First of all, Sigma Chi is a fraternity, and your sister could not have been a member. She was probably a member of a “little sisters” association which is a group of women associated with the fraternity. These organizations faded away some time ago as described in the following article:
At our fraternity, the little sisters group was about a quarter the size of the fraternity, and was made up of a mixture of unaffiliated women who choose not to join a sorority, the girlfriends of brothers, or siblings of brothers. Since men were not generally allowed in sororities, these groups started because the only place sorority women could only hang out with their fraternity boyfriends was at the fraternity house.
“Little sister” groups allowed the women a formal place within the fraternity organization. There was a rush involved, and specific events were held for them, but they couldn’t live in the house or be full members. Their role was not subservient, but more auxiliary in nature. In fact, at our house, in addition to picking a “big brother”, a new pledge was supposed to pick a “big sister” to help guide him through the college years.