In many cases where IEF is used it seems far too complicated for users to set "published" / "unpublished" on very IEF element. It would be nice to have a further option in the field settings to show / hide that on field basis.
Of course this can be done by a hook but in my opinion this feature would help many many IEF users. We've disabled that field in nearly every project.
Perhaps related to: #2176879: Availability of all "Publishing options" →
Closed: won't fix
1.0
Code
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It's likely this issue predates Contrib.social: some issue and comment data are missing.
Due to limited developer time old feature requests for IEF are being closed. If you still have a need for this functionality, then you may feel free to reopen the issue. But please note that if you are still using Drupal 7 and would like for this functionality to be added to the D7-compatible version of IEF, then our limited resources and lack of interest may prevent that from ever happening.