= Non-logical particle (+ subject), that gets left out due to context
Explanation
In English, the equivalent would be “he” or “she” (…) to avoid repeating the subject. For example:
Tom went to school. Then, he went home. Also, he made his homework.
The ∅ is essentially the same, however it does not get written down/spoken:
トムさんが大学に行った。そして、(トムさんが) 家に帰った。また、(トムさんが) 宿題をした。