The behavior is controled by the option replicate deletion as un-label / archive:

If you enable the option replicate deletion as un-label / archive, the replication of deletion of emails will work as follows:

1. if user A deletes an email (puts it in the trash or permanently deletes it) then user B will have that email archived.
2. if user A un-labels an email message then user B will have that email message also unlabeled.
3. if user A deletes the label (and does not trash/delete email messages from the label), then user B will also have that label gone. User B will see email messages unlabeled.

If you disable the option replicate deletion as un-label / archive, the replication of deletion of emails will work as follows:

1. if user A deletes an email (puts it in the trash or permanently deletes it) then user B will have that email in the Gmail trash.
2. if user A un-labels an email message, then user B will have that email message also unlabeled.
3. if user A deletes the label (and does not trash/delete email messages from the label), then user B will also have that label gone. User B will see email messages unlabeled.