The option If an email is deleted (moved to trash), we will only remove its label instead of moving it to the trash. controls this behavior:

When this setting is enabled:

1. If user A deletes an email (moves to trash or deletes forever), it will be archived for user B.
2. If user A removes a label from an email, user B will also see it without the label.
3. If user A deletes a label but not the emails, user B loses the label too. Emails will show up without labels for user B.

When this setting is disabled:

1. If user A deletes an email (moves to trash or permanently deletes it), it goes to user B’s Gmail trash.
2. If user A removes a label from an email, user B also sees it without the label.
3. If user A deletes a label without deleting the emails, user B loses the label too. Emails become unlabeled for user B.

In summary, a shared group member will only see an email in the trash if another member moves it to trash or deletes it permanently.