Do you have an example on hand to provide further context? There are differing ideas behind the usage of Ↄ but with references to names I can think of one.

The Ↄ mark itself is reported by Quintilian (Institutes of Oratory. 1.7.28) as being a reference to a woman (unnamed most likely). He suggests this is because women were referred to as Gaiae, and the letter C referenced the name Gaius, thus inverted it was considered the feminine version. Roman Republican women for the most part took on the feminine version of their family name (Julia, Cornelia etc.).

Ↄ.I could be referring to a freed female possibly upon the list. With an example it may be easier to understand the context better.