"Abdicating her agency" means she gave up making her own decisions. For example, if this man she was following stayed in a certain hotel, she would stay in the same one, she would eat at the same restaurants, she would wake up when he woke up and go to bed when he went to bed. So would "stick to him like glue" and his life patterns would become her life patterns. The person she was would become lost, and she would become a new person who was dedicated to following this man's tracks.

It‘a hard to say exactly without even bigger context, but from what I can read it’s more like this; “abdicate her agency” - abdicate means to renounce, or to fail to undertake a responsibility. “Agency” doesn’t just mean a business or organisation, but often refers to a persons free-will, their right to act and make choices autonomously. So I’m inclined to believe that the full expression means that she gave up her own freedom to follow this man (although it is possible that if she had a business/organisation) then it means she gave that up. You’re more or less right about the second one, however that she go “lost” suggests that she really gave up her sense-of-self.