When a post is deleted in the Publication, it is not automatically removed from the Niche. Removal from the Publication transfers the content post control from the Publication to the Content Creator. The only reason that it would be removed from the Niche is if the post is not appropriate to the Niche. The Niche moderators are the gatekeepers for Niches.
Please note that if the writer submits to the Publication and the Niches simultaneously, the Publication editor is given control of the post. It is not automatically tagged to the Niches until the Publication editor approves and accepts the post. This is because the Publication editor can change the Niches while they are in control. If during this scenario, the Publication editor decides to reject the post, the post control is sent back to the writer and the post appears in their "draft" posts. This is because the writer is given an open to edit it again (since it was not accepted by Publication) before it is posted to the Niches. Technically, it was not removed from the Niche as it was not formally placed there during the Publication submittal process.