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

If you turn on the replicate deletion as un-label / archive setting, here’s how email deletions are handled:

1. If user A deletes an email (either moves it to trash or deletes it permanently), then it will be archived for user B.
2. If user A removes a label from an email, user B will also see that email without the label.
3. If user A deletes a label without trashing the emails in it, then user B will lose that label too. For user B, those emails will appear without any labels.

If you turn off the replicate deletion as un-label / archive setting, here’s what happens with email deletions:

1. If user A deletes an email (either by moving it to trash or by deleting it permanently), then that email will end up in user B’s Gmail trash.
2. If user A removes a label from an email, user B will see the email without the label as well.
3. If user A deletes a label without deleting the labeled emails, user B will also lose that label. Those emails will be unlabeled for user B.

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