If you view the Media Library in the list mode:
/wp-admin/upload.php?mode=list
then you will see the Attach/Detach links for each attachment.
Each attachment can only be attached to a single parent through the post_parent
field in the wp_posst
table.
Deleting an image from the post editor will not change the post_parent
field to 0.
Making life a little bit easier!
It would be nice to be able to do it within the Media View popup, when editing a post, since it can take a long time to find it within the media library.

First we construct a custom Backbone micro template, that we will add to the Attachment Details view:
<script type="text/html" id="tmpl-wpse-open-in-library">
<div class="wpse-open-in-library">
<a href="<?php echo admin_url('upload.php?mode=list&p=');?>{{ data.id }}" target="_blank">
<?php _e( 'Open in Media Library' ); ?>
</a>
</div>
</script>
where {{ data.id }}
is the current attachment's ID.
This is how we insert it after the Delete Attachment link:
$( wp.media.template('wpse-open-in-library')(
{
id: attachment.get( 'id' ) // <-- This is how we can fetch the current ID
}
)
).insertAfter('.delete-attachment');
where we pass the id
variable to our custom micro template.
Note that we can view all the attached files by selecting the following option:

Demo plugin
Here's the whole demo plugin:
/**
* Open an attachment in the Media Library, to be able to attach/detach it
*
* @link https://wordpress.stackexchange.com/a/206179/26350
*/
add_action( 'print_media_templates', function()
{ ?>
<!-- Custom template part -->
<script type="text/html" id="tmpl-wpse-open-in-library">
<div class="wpse-open-in-library">
<a href="<?php echo admin_url('upload.php?mode=list&p=');?>{{ data.id }}" target="_blank">
<?php _e( 'Open in Media Library' ); ?>
</a>
</div>
</script>
<!-- Extend the Attachment Details View -->
<script>
jQuery(document).ready( function( $ )
{
wp.media.view.Settings.AttachmentDisplay = wp.media.view.Settings.AttachmentDisplay.extend(
{
render: function()
{
wp.media.View.prototype.render.apply( this, arguments );
var attachment = this.options.attachment;
$( wp.media.template('wpse-open-in-library')(
{
id: attachment.get( 'id' )
}
)
).insertAfter('.delete-attachment');
return this;
}
} );
} );
</script>
<?php
} );
This answer by @kalimah-apps and the answers here by @bonger and @Fabien Quatravaux, were of great help construction this demo plugin.
Then the next step would be to add the Detach link, to make it even easier ;-)