I always used e.g. to introduce a non-exhaustive list, as in the following sentence.
He was the school champion of many activities (e.g., chess, badminton, 110m hurdles, and high jump).
Can e.g. be used to introduce a clause?
This can be used by other modules to act accordingly, e.g. field_ui uses it to add operation links to manage fields and displays.
This is what the former CEO's did too, e.g. John Doe did it when he was CEO between 2001 and 2006.