Historically, I've controlled almost 100% of the theming work on my site, and everything else has been other admins. I've recently been working with a team to provide them with theme access to a group that they oversee. I've given those team members Owner permissions on their group and instructions on how to change what they need to. Since they're not full site admins, we encountered what I would consider a bug, but wanted to share it here to give the Verint team a chance to review and also alert fellow admins.
In this group, I used a few Unfiltered HTML widgets (and also the Group Description widget) for some customizations to the interface. As an admin, I've previewed/published without issue. However, when these team members tried, they would see these widgets locked (my admin view with the specific widgets in orange and their view in red):
The problem is when these non-admins would publish the page, the 3 locked widgets (above) are removed. The bottom Unfiltered HTML widget (the full-page footer one) includes CSS styling that affects this group home page, so its removal effectively broke the page, unbeknown to the non-admin team member who was modifying the Featured Content widget on the same page.
I was able to work around this as described in RE: Unfiltered HTML - Locked for Group Owner, Not for Admin, however, I'd expect the behavior to be that the user cannot edit the locked widgets, but they'd remain as-is after publishing.